<PAGE>
                                                                    EXHIBIT 10.2



                              AMENDED AND RESTATED
                   EMPLOYMENT AGREEMENT OF RICHARD R. BURNHAM

         THIS AMENDED AND RESTATED EMPLOYMENT AGREEMENT Is made and entered into
effective as of the 28th day of February, 2002 (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, the Company entered into that certain Employment Agreement
dated March 1, 1999 (the "Original Employment Agreement"), by and between the
Company and Employee pursuant to which Employee has served as the President and
Chief Executive Officer of the Company;

         WHEREAS, Employee has acquired special and unique knowledge, abilities
and expertise with respect to the business of the Company; and

         WHEREAS, the Board of Directors of the Company (the "Board") has
determined that it is in the best interests of the Company and its stockholders
to continue the employment of Employee as the Chief Executive Officer of the
Company and, accordingly, the Company and Employee desire to amend and restate
the Original Employment Agreement as set forth herein.

         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 Chief Executive Officer of the Company. Employee shall report to
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.

<PAGE>


         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 Sections 4, 5 and 6 hereof, Employer shall pay
Employee an initial salary of $400,000.00 per year, payable on a semi-monthly
basis in accordance with Employer's regular payroll practices. Employee's
compensation shall be reviewed annually by the Compensation Committee of the
Board.

         Employee shall receive an automobile allowance of $1,300.00 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 Employer'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 within five (5) business days after the
determination of the amount due, such determination being made no later than the
date each calendar year on which the Company publicly announces its earnings for
the prior fiscal year in a press release.

         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, the 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



                                       2
<PAGE>

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. NONCOMPETITION AGREEMENT. (a) Employee recognizes that Employer has
been induced to enter into this Agreement primarily because of the covenants and
assurances made by Employee, that Employee's covenant not to compete is
necessary to insure continuation of the 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 during the Term of Noncompetition Employee shall not directly or
indirectly:

                  (i) 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 (A) 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
(B) is engaged in the same business as Employer anywhere within a 50-mile radius
of the location of any of Employer's facilities;

                  (ii) 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

                  (iii) Solicit or encourage any employee, volunteer, officer or
director to leave Employer or hire any employee, volunteer, officer or director
of Employer.

         (b) The "Term of Noncompetition" means the period of time beginning on
the date hereof and continuing until (i) 5:00 p.m., Dallas, Texas time, on the
first anniversary of the date of termination of Employee's employment if
Employee's employment is terminated either (A) by Employer by reason of
Employee's long-term disability (as defined in Section 7.2(b)) pursuant to
Section 7.2(b) or (B) by Employer for Cause (as defined in Section 7.2(c))
pursuant to Section 7.2(c); (ii) if Employee's employment is terminated by
Employer without Cause pursuant to Section 7.2(d) or Section 7.3(a), or Employee
resigns for Good Reason pursuant to Section 7.2(e)(i) or Section 7.3(b), 5:00
p.m., Dallas, Texas time, on the later to occur of (A) the first anniversary of
the date of termination of Employee's employment or (B) the last day of the
Severance Period (as defined in Section 7.2(d)(i)); or (iii) 5:00 p.m., Dallas,
Texas time, on the second anniversary of the date of termination of Employee's
employment if Employee resigns without Good Reason pursuant to Section
7.2(e)(ii).

         (c) 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 be enforced in its place, and the remaining restrictions contained
herein shall be enforceable independently of each other.



                                       3
<PAGE>

         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.,
Dallas, Texas time, on February 28, 2005, 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, 2005, 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, with 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 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;



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<PAGE>

                           (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;

                           (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:

                           (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 the Severance Period (as defined below);

                           (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. "COBRA"
means the Consolidated Omnibus Budget Reconciliation Act of 1985, as amended.
Employee is solely responsible for properly and timely electing COBRA coverage;
and

                           (iv) With respect to any stock options granted to
Employee that are not vested as of the date of Employee's termination of
employment pursuant to this Section 7.2(d), these options shall vest in full as
of the date of Employee's termination of employment hereunder and, in addition,
all stock options owned by Employee as of the date of Employee's termination of
employment pursuant to this Section 7.2(d) shall remain exercisable for a period
of two years from and after the date of Employee's termination of employment
hereunder



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<PAGE>

(notwithstanding anything to the contrary contained in the stock option
agreement(s) evidencing such stock options).

                  Employee's right to receive these severance benefits is
conditioned on his compliance with the obligations in Section 6. "Severance
Period" means the period of time beginning on Employee's date of termination of
employment pursuant to this Section 7.2(d) and continuing until the earlier to
occur of (A) 5:00 p.m., Dallas, Texas time, on the second anniversary of the
date of termination of Employee's employment pursuant to this Section 7.2(d) or
(B) the date the Employee obtains employment with any entity. If Employee
secures employment with another entity before his termination from the Employer,
the Severance Period shall consist of zero days. In the case of a termination
without Cause, where Employee's new employer does not maintain health insurance
for Employee, Employee shall be entitled to continued health benefits pursuant
to Section 7.2(d)(iii) for the Severance Period which for this purpose shall be
determined on the basis that employment with an employer that does not maintain
health insurance does not satisfy clause (B) of the definition of "Severance
Period." Notwithstanding the foregoing provisions of this Section 7.2(d), this
Section 7.2(d) shall be applied in a manner consistent with COBRA.

                  (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;

                                    (2)     A material breach by Employer of
this Agreement; or

                                    (3)     Employee is required to move his
residence to a location that is more than 50 miles from his current residence.

                           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.

                  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



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<PAGE>

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 7.3 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 7.3, 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 for 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; or



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<PAGE>

                           (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 HealthCare, Inc.
                  4705 Villa Vera Drive              717 North Harwood, Suite 1500
                  Arlington, Texas 76017             Dallas, Texas 75201

                                                     with a copy to:
                                                     P. Gregory Hidalgo
                                                     Vinson & Elkins L.L.P.
                                                     3700 Trammell Crow Center
                                                     2001 Ross Avenue
                                                     Dallas, Texas 75201
</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.



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<PAGE>

                  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 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 in 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 contains the entire
agreement between the parties concerning the subject matter hereof and
supersedes all previous contracts or agreements (including, without limitation,
the Original Employment Agreement), understandings, discussions, negotiations
and undertakings, whether written or oral, between the parties with respect
thereto. 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



                                       9
<PAGE>

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.

                  [REMAINDER OF PAGE INTENTIONALLY LEFT BLANK]



                                       10
<PAGE>

         IN WITNESS WHEREOF, the parties have executed this Agreement as of the
date first above written.

                   EMPLOYER:       Odyssey HealthCare, Inc.



                                   By:      /s/ Doug Cannon
                                       ----------------------------------------
                                   Name:        Doug Cannon
                                        ---------------------------------------
                                   Title:       SVP -- CFO
                                           ------------------------------------



                   EMPLOYEE:                /s/ Richard R. Burnham
                                   --------------------------------------------
                                   Richard R. Burnham