EMPLOYMENT AGREEMENT OF RICHARD R. BURNHAM
 
 
         THIS EMPLOYMENT AGREEMENT is made and entered into as of the 1st day of
March 1999 (the "Effective Date") between Odyssey HealthCare, Inc., a Delaware
corporation ("Employer" or the "Company"), and Richard R. Burnham, residing at
4705 Villa Vera Drive, Arlington, Texas 76017 ("Employee"),
 
                                   WITNESSETH:
 
         WHEREAS, Employer has employed Employee as President and Chief
Executive Officer since August 29, 1995;
 
         WHEREAS, Employer desires to retain the services of Employee, and
Employee desires to be employed by Employer, upon the terms and conditions
hereinafter set forth;
 
         WHEREAS, as an ancillary and integral part of this Agreement, Employer
desires to obtain Employee's covenant not to compete and other covenants, and
Employee desires to make a covenant not to compete and such other covenants as
hereinafter set forth;
 
         NOW, THEREFORE, in consideration of the premises and agreements herein
contained, and other good and valuable consideration, the receipt and adequacy
of which are hereby forever acknowledged and confessed, the parties agree as
follows:
 
         1. EMPLOYMENT. Employer hereby employs Employee, and Employee hereby
accepts such employment by Employer, upon the terms and conditions specified
herein for the "Term of Employment" (as hereinafter defined).
 
         2. DUTIES OF EMPLOYEE. During the Term of Employment, Employee shall be
employed as the President and Chief Executive Officer of the Company. Employee
shall report to the Board of Directors of Employer (the "Board"). Employee shall
perform such duties as are appropriate for the offices to which he has been
appointed hereunder, as well as such other duties consistent with such offices
that may be assigned from time to time by the Board in its sole discretion.
During the Term of Employment, Employer shall nominate Employee, and use its
best efforts to cause Employee to be elected, as a member of the Board and the
Executive Committee of the Board. Employee shall, subject to the direction and
instruction of Employer, (a) devote Employee's full and entire working time,
attention and energies to Employer, and diligently and to the best of Employee's
ability perform all duties incident to Employee's employment hereunder; (b) use
Employee's best efforts to promote the interests of Employer and (c) perform
such other duties appropriate for Employee's position as Employer may from time
to time direct.
 
         3. FINANCIAL ARRANGEMENTS.
 
                  3.1 Compensation. As compensation for Employee's services
hereunder and in consideration of Employee's covenant not to compete and other
covenants as set forth in
 
 
 
<PAGE>   2
 
Sections 4, 5 and 6 hereof, Employer shall pay Employee an initial salary of
$210,600.00 per year, payable on a semi-monthly basis in accordance with
Employer's regular payroll practices.
 
         Employee shall receive an automobile allowance of $900.00 per month and
shall be reimbursed for all the actual costs and expenses incurred by him in the
performance of his duties. Employee shall be entitled to three (3) weeks paid
vacation time each year and other benefits (e.g., sick leave and health
insurance) in accordance with Employee's policies as from time to time
established for executive officers of Employer.
 
                  3.2 Bonus. In addition to the salary payable to Employee,
Employee shall be entitled to an annual bonus. The bonus will be determined
annually by the Compensation Committee of the Board and Employee based on goals
that are mutually agreed by the Compensation Committee of the Board and
Employee. The bonus shall be payable upon determination of the amount due, of
each calendar year for the prior calendar year of Employer, which shall be the
earlier of completed audited financials or March 15th.
 
         4. CONFIDENTIALITY. Employee agrees to keep confidential and not to use
or to disclose to others, except as expressly consented to in writing by
Employer, or as required by law to be disclosed, any trade secrets, confidential
technology, proprietary information, customer information, business plans, or
other knowledge belonging to or relating to the affairs of Employer or any
subsidiary or parent of Employer (an "Affiliate"), or any knowledge or thing
acquired or developed by Employee through Employee's association with Employer
or an Affiliate, to use or disclosure of which knowledge or thing might
reasonably be construed to be contrary to the best interests of Employer or an
Affiliate. Employee further agrees that upon the termination of Employee's
employment, Employee shall promptly return, and will neither take nor retain
without prior written authorization from Employer, any papers, data, client
lists, books, records, files, computer data or other documents (or copies
thereof) or materials of any kind belonging to Employer or an Affiliate or
pertaining to the business of Employer or an Affiliate. This covenant shall be
perpetual and shall survive the termination or expiration of this Agreement.
 
         5. ITEM OWNERSHIP. All patents, formulae, inventions, ideas of
inventions, processes, copyrights, know-how, proprietary information,
trademarks, tradenames or other developments, or future improvements thereto
(collectively, "Items"), developed or conceived by Employee during the term of
this Agreement are the property of Employer and shall be promptly disclosed to
Employer. Employee shall further execute an assignment of the Items to Employer
and execute such other instruments as Employer shall reasonably request to
protect Employer's interest in the Items. Employee represents that his
performance of this Agreement does not and will not breach any agreement to keep
in confidence items acquired by him in confidence or in trust prior to his
employment with Employer. Employee agrees not to disclose to Employer or induce
Employer to use any Items belonging to any previous employer or others. Employee
further agrees not to enter into any agreement, either written or oral, in
conflict herewith. This covenant shall be perpetual and shall survive the
termination or expiration of this Agreement.
 
         6. NON-COMPETITION AGREEMENT. Employee recognizes that Employer has
been induced to enter into this Agreement primarily because of the covenants and
assurances made by Employee, that Employer's covenant not to compete is
necessary to ensure continuation of the
 
 
 
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<PAGE>   3
 
business of Employer, and that irreparable harm and damage will be done to
Employer if Employee competes with Employer within the geographic areas
described below. Therefore, Employee agrees that for so long as he is employed
by Employer, and for a period of 12 months thereafter, Employee shall not
directly or indirectly:
 
                  (a) Own, manage, operate, control, participate in the
management or control of, be employed by, lend Employee's name to or maintain or
continue any interest whatsoever in any enterprise that (i) provides,
distributes, markets, promotes or advertises any type of services or products
that directly competes with the services or products offered by Employer, and/or
(ii) is engaged in the same business as Employer anywhere within a 50-mile
radius of the location of any of Employer's facilities;
 
                  (b) Solicit, interfere with, divert or attempt to divert any
business relationships of Employer, including without limitation, its customers,
clients, patients, sponsors, partners, or suppliers; or
 
                  (c) Solicit or encourage any employee, volunteer, officer or
director to leave Employer.
 
         If any restriction contained in this Section 6 is held by any court to
be unenforceable or unreasonable, a lesser restriction shall be severable
therefrom and enforced in its place, and the remaining restrictions contained
herein shall be enforceable independently of each other.
 
         7. TERM AND TERMINATION OF AGREEMENT.
 
                  7.1 TERM OF EMPLOYMENT.
 
                  (a) Basic Term. As used herein, "Term of Employment" shall
mean the period commencing on the Effective Date and expiring at 12:00 A.M. CST
on February 28, 2002, as extended under Section 7.1(b).
 
                  (b) Renewal. The Term of Employment will be renewed
automatically for an additional one (1) year period (without any action by
either party) on February 28, 2002, and on each anniversary thereof, unless one
party gives to the other written notice sixty (60) days in advance of the
beginning of any one-year renewal period that the Agreement will not be renewed.
Either party may elect not to renew this Agreement, without or without Cause, in
which case Employee's employment hereunder shall terminate effective on the last
day of the Term of Employment, and Employer shall pay to Employee all
compensation due Employee pursuant to Section 3 through the date of termination
and thereafter shall have no further obligation to Employee hereunder. Nothing
stated in this Agreement or represented orally or in writing to either party
shall create an obligation to renew this Agreement.
 
                  7.2 TERMINATION.
 
                  (a) Death. Employee's employment hereunder shall terminate
immediately upon Employee's death. If Employee's employment is terminated as a
result of his death, Employer shall pay to the estate of Employee, or his
beneficiaries, all compensation due Employee pursuant to Section 3 through the
date of Employee's death, and thereafter shall have
 
 
 
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<PAGE>   4
 
no further obligation to Employee hereunder other than pursuant to any life
insurance policies that may be in effect for the benefit of Employee or his
beneficiaries.
 
                  (b) Long-Term Disability. If Employee suffers a long-term
disability (as hereinafter defined), Employer may, to the extent permitted by
law, terminate Employee's employment hereunder, which shall be effective
immediately upon written notice. Employee's base salary pursuant to Section 3
shall be continued during the remainder, if any, of the first six months of such
Long-Term Disability following Employee's termination, and thereafter Employer
shall have no further obligation to Employee hereunder. A "long-term disability"
is an illness, accident or other physical or mental incapacity that has
prevented or will prevent Employee from performing the essential functions of
his employment position without an accommodation that would not be an undue
hardship for Employer to provide. The foregoing definition of long-term
disability is not intended to and shall not affect the definition of
"disability" or any similar term in any insurance policy Employer may provide.
 
                  (c) For Cause. Employer may terminate Employee's employment
hereunder at any time, effective immediately upon notice, for "Cause." As used
herein, "Cause" shall mean:
 
                           (i) Conduct which is in bad faith, dishonest or in
breach of his fiduciary duty and could be materially detrimental to Employer;
 
                           (ii) Conduct which constitutes a felony involving
dishonesty, breach of trust, or physical or emotional harm to any person;
 
                           (iii) Refusing or failing to act in accordance with
any lawful direction or order of the Board of Directors;
 
                           (iv) Exhibiting in regard to his employment gross
negligence, misconduct, habitual neglect, or incompetence; or
 
                           (v) A breach of any material term of this Agreement.
 
         For purposes of this Section, Employee's conduct shall not constitute
Cause for termination unless Employee is unable to cure the grounds for
termination within 30 days after written notice from Employer, and if Employee's
conduct is caused by a Long-Term Disability, Section 7.2(b) above shall control,
and not this subsection on termination for Cause. If Employee is terminated for
Cause, Employer shall pay to Employee all compensation due Employee pursuant to
Section 3 through the date of termination and thereafter shall have no further
obligation to Employee hereunder.
 
                  (d) Without Cause. Employee's employment hereunder may be
terminated by Employer at any time without Cause, effective upon 30 days prior
written notice of termination. If Employer shall terminate Employee's employment
hereunder without Cause, then Employer shall provide Employee with the following
severance benefits and, thereafter, shall have no further obligation to Employee
hereunder:
 
 
 
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<PAGE>   5
 
                           (i) Employer shall continue to pay to Employee an
amount equal to the base salary to which Employee would be entitled pursuant to
Section 3 at the time of termination, which shall be payable on the regularly
scheduled paydays and in accordance with Employer's regular payroll practice for
12 months (the "Severance Period");
 
                           (ii) Employer shall pay Employee a pro-rated amount
of any annual bonus to which Employee would be entitled, which shall be paid at
the earlier of (1) the date it would have been due if employee was not
terminated, or (2) upon completion of the Severance period. Employee shall not
be entitled to any other bonus payments;
 
                           (iii) Employer shall reimburse Employee for any COBRA
payments actually incurred by Employee during the Severance Period. Employee is
solely responsible for properly and timely electing COBRA coverage; and
 
                           (iv) With respect to any non-vested stock options
granted to Employee as of March 1, 1999, these options shall vest as of the date
of Employee's termination of employment hereunder and all stock options owned by
Employee under grants prior to March 1, 1999, shall remain exercisable for a
period of two years from and after the date of Employee's termination of
employment hereunder.
 
         Employee's right to receive these severance benefits is conditioned on
his compliance with the obligations in Section 6.
 
                  (e) By Employee.
 
                           (i) Employee may voluntarily terminate his employment
at any time for "Good Reason". As used herein, "Good Reason" shall mean:
 
                                    (1) A reduction in the compensation paid to
Employee below the compensation provided in Section 3.1, other than a reduction
comparable to reductions generally applicable to similarly situated employees;
or
 
                                    (2) A material breach by Employer of this
Agreement;
 
                                    (3) Employee is required to move his
residence to a location that is more than 50 miles from his current address.
 
         If Employee voluntarily terminates his employment for "Good Reason",
Employer shall provide Employee the same severance benefits as described under
Section 7.2(d) and thereafter shall have no further obligation to Employee
hereunder.
 
                           (ii) Employee may voluntarily terminate his
Employment at any time without a "Good Reason". If Employee terminates his
employment without a "Good Reason", Employer shall pay to Employee all
compensation due Employee pursuant to Section 3 through the date of termination
and thereafter shall have no further obligation to Employee hereunder.
 
 
 
                                       5
<PAGE>   6
 
                  7.3 TERMINATION FOLLOWING A CHANGE OF CONTROL.
 
                  (a) By Employer Without Cause. If Employer terminates
Employee's employment hereunder without Cause and within two years following a
Change of Control (as defined below), Employer shall provide Employee with the
severance benefits provided in Section 7.2(d) except that the Severance Period
shall be the greater of (A) the remainder of the two years following the Change
of Control following the effective date of termination and (B) the Severance
Period provided in Section 7.2(d). For the purposes of this Section only, Cause
shall be limited to:
 
                           (i) The willful engaging by Employee in conduct which
is materially injurious to Employer, monetarily or otherwise, and the failure to
cure such conduct within 30 days after written notice from Employer;
 
                           (ii) Employee's conviction of or plea of nolo
contendre to a felony; or
 
                           (iii) A willful breach of Sections 4, 5 or 6 of this
Agreement.
 
         For the purposes of this Section, no conduct shall be deemed "willful"
unless engaged in without good faith and without reasonable belief that the
conduct is in the best interest of Employer.
 
                  (b) By Employee for Good Reason. If Employee terminates his
employment hereunder without Good Reason and within two years following a Change
of Control (as defined below), Employer shall provide Employee with the
severance benefits provided in Section 7.2(d) except that the Severance Period
shall be the greater of (A) the remainder of the two years following the Change
of Control following the effective date of termination, and (B) the Severance
Period provided in Section 7.2(d). For the purposes of this Section only, Good
Reason shall mean the definitions included in Section 7.2(e)(i) or any of the
following:
 
                           (i) A material change in Employee's position, duties,
authority or reporting responsibilities as set forth in Section 2 above to the
detriment of Employee; or
 
                           (ii) A relocation of Employee's workplace of at least
50 miles.
 
                  (c) Definition of Change of Control. For the purposes of this
Agreement, a "Change of Control" shall mean any of the following events:
 
                           (i) The consummation of any consolidation or merger
of Employer with another corporation or entity, and as a result of such
consolidation or merger, less than fifty percent (50%) of the outstanding voting
securities of the surviving or resulting corporation or entity shall be owned in
the aggregate by the stockholders of Employer as the same shall have existed
immediately prior to such consolidation or merger;
 
                           (ii) The consummation of any sale, lease, exchange or
other transfer (in one transaction or a series of related transactions) of all,
or substantially all, of the assets of Employer;
 
                           (iii) The approval by the stockholders of Employer of
any plan or approval for the liquidation or dissolution of Employer;
 
 
 
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<PAGE>   7
 
                           (iv) Any "person" (as such term is used in Sections
13(d) and 14(d)(2) of the Securities Exchange Act of 1934, as amended) becomes
the "beneficial owner" (within the of Section 13d-3 under said Act) of fifty
percent (50%) or more of Employer's outstanding voting securities, without the
approval of the Board.
 
         8. ARBITRATION. Any dispute between Employee and Employer (including
any of its Affiliates, directors, employees or agents) relating to Employee's
employment shall be settled by arbitration in accordance with the employment
dispute resolution rules of the American Arbitration Association then in effect.
This arbitration clause applies to all claims relating to Employee's employment,
including without limitation, contract claims, tort claims and claims under
federal, state or local statutes or ordinances (for example, Title VII, the Age
Discrimination in Employment Act, and the Americans with Disabilities Act). The
arbitrator may grant any relief available under applicable law. The decision of
the arbitrator shall be final and binding on the parties to the arbitration and
shall be the exclusive remedy for all such disputes. Judgment may be entered on
the arbitrator's decision in any court having jurisdiction. This covenant shall
be perpetual and shall survive the termination or expiration of this Agreement.
THE PARTIES HEREBY WAIVE ANY RIGHTS THEY MAY HAVE TO TRIAL BY JURY IN REGARD TO
DISPUTES COVERED BY THIS ARBITRATION CLAUSE.
 
         9. ADDITIONAL PROVISIONS.
 
                  9.1 Notices. Any notice, demand, or communication required,
permitted, or desired to be given hereunder, shall be deemed effectively given
when personally delivered or mailed by prepaid, certified mail, return receipt
requested, addressed as follows:
 
<TABLE>
<CAPTION>
                  Employee                           Employer
                  --------                           --------
 
<S>                                                 <C>
                  Richard R. Burnham                 Odyssey Health Care, Inc.
                  4705 Villa Vera Drive              71 North Harwood, Suite 2580
                  Arlington, Texas 76017             Dallas, Texas 75201-6538
 
                                                     with a copy to:
                                                     Tom E. Wilson, Esq.
                                                     Morrison & Foerster LLP
                                                     755 Page Mill Road
                                                     Palo Alto, CA 94304-1018
</TABLE>
 
         or to such other address, and to the attention of such other person(s)
or officer(s) as either party may designate by written notice.
 
                  9.2 Governing Law. This Agreement has been executed and
delivered in, and shall be interpreted, construed, and enforced pursuant to and
in accordance with the laws of the State of Texas.
 
                  9.3 Assignment. This Agreement and the rights and obligations
hereunder shall bind and inure to the benefit of any successor or successors of
Employer by way of reorganization, merger or consolidation, and any assignee of
all or substantially all of its business
 
 
 
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<PAGE>   8
 
and properties, but, except as to any such successor or assignee of Employer,
neither this Agreement nor any rights or benefits hereunder may be assigned by
either party.
 
                  9.4 Waiver of Breach. The waiver by either party of a breach
or violation of any provision of this Agreement shall not operate as, or be
construed to be, a waiver of any subsequent breach of the same or other
provision hereof.
 
                  9.5 Enforcement. Without limiting other possible remedies to
Employer for the breach of this Agreement, Employee agrees that injunctive or
other equitable relief shall be available to enforce the covenants set forth in
Section 4, 5 and 6, such relief to be without the necessity of posting a bond,
cash or otherwise.
 
                  9.6 Gender and Number. Whenever the context hereof requires,
the gender of all words shall include the masculine, feminine and neuter, and
the number of all words shall include the singular and plural.
 
                  9.7 Additional Assurances. The provisions of this Agreement
shall be self-operative and shall not require further agreement by the parties
except as may be herein specifically provided to the contrary; provided,
however, at the request of Employer, Employee shall execute such additional
instruments and take such additional acts as Employer may deem necessary to
effectuate this Agreement.
 
                  9.8 Severability. If any provision of this Agreement is held
to be unenforceable for any reason, the unenforceability thereof shall not
affect the remainder of this Agreement, which shall remain in full force and
effect and enforceable in accordance with its terms. Employee further agrees
that if any restriction contained in any Section is held by any court to be
unenforceable or unreasonable, a lesser restriction shall be enforced in its
place and all remaining restrictions contained herein shall be enforced
independently of each other.
 
                  9.9 Headings. The headings contained this Agreement are for
reference purposes only and shall not affect in any way the meaning or
interpretation of this Agreement.
 
                  9.10 Withholdings. All amounts in this Agreement shall be paid
less applicable payroll deductions.
 
                  9.11 Entire Agreement. This Agreement supersedes all previous
contracts or agreements, including without limitation the Employment Agreement
executed by the parties on August 29, 1995, and constitutes the entire agreement
between the parties. No oral statements or prior written material not
specifically incorporated herein shall be of any force and effect, and no
changes in or additions to this Agreement shall be valid unless in writing and
signed by the parties hereto. Employee specifically acknowledges that in
entering into and executing this Agreement, Employee relies solely upon the
representations and agreements contained in this Agreement and no others.
 
 
 
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<PAGE>   9
 
         IN WITNESS WHEREOF, the parties have executed this Agreement as of the
date first above written.
 
                    EMPLOYER:                Odyssey HealthCare, Inc.
 
                                                  /s/ Mark Wan
                                             -----------------------------------
 
                                             By:  Mark Wan
                                                --------------------------------
 
                                             Its: Director
                                                 -------------------------------
 
 
 
                    EMPLOYEE:                     /s/ Richard R. Burnham
                                             -----------------------------------

                                             Richard R. Burnham