<PAGE>   1
                                                                EXHIBIT 10.10.2



         THIS WARRANT AND THE SECURITIES ISSUABLE UPON THE EXERCISE HEREOF HAVE
         NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED. THEY
         MAY NOT BE SOLD, OFFERED FOR SALE, PLEDGED, HYPOTHECATED, OR OTHERWISE
         TRANSFERRED EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT
         UNDER SUCH ACT, OR AN OPINION OF COUNSEL SATISFACTORY TO THE COMPANY
         THAT REGISTRATION IS NOT REQUIRED UNDER SUCH ACT, OR UNLESS SOLD
         PURSUANT TO RULE 144 UNDER SUCH ACT.


                              WARRANT TO PURCHASE
                      SERIES B CONVERTIBLE PREFERRED STOCK
                                       OF
                            ODYSSEY HEALTHCARE, INC.

                            VOID AFTER MAY 21, 2008


                  This Warrant is issued to ___________________, or its
registered assigns ("Holder") by Odyssey HealthCare, Inc., a Delaware
corporation (the "Company"), on May 22, 1998 (the "Warrant Issue Date") at a
purchase price of $.025 for each share of Preferred Stock (as defined below)
that this Warrant is originally exercisable. This Warrant is issued pursuant to
the terms of that certain Promissory Note and Warrant Purchase Agreement dated
as of the date hereof (the "Purchase Agreement").

                  1. Purchase of Shares. Subject to the terms and conditions
hereinafter set forth and set forth in the Purchase Agreement, the Holder is
entitled, upon surrender of this Warrant at the principal office of the Company
(or at such other place as the Company shall notify the holder hereof in
writing), to purchase from the Company up to ________________ (_________) fully
paid and nonassessable shares of Series B Convertible Preferred Stock of the
Company (the "Preferred Stock"). The number of shares of Preferred Stock
issuable pursuant to this Section 1 (the "Shares") shall be subject to
adjustment pursuant to Section 8 hereof.

                  2. Exercise Price. The purchase price for the Shares shall be
$1.25, as adjusted from time to time pursuant to Section 8 hereof (the
"Exercise Price").

                  3. Exercise Period. This Warrant shall be exercisable, in
whole or in part, during the term commencing on the Warrant Issue Date and
ending at 5:00 p.m. on May 21, 2008; provided, however, that in the event of
(a) the closing of the Company's sale or transfer of all or substantially all
of its assets or (b) the closing of the acquisition of the Company by another
entity by means of merger, consolidation or other transaction or series of
related transactions, resulting in the exchange of the outstanding shares of
the Company's capital stock such that the stockholders of the Company prior to
such transaction own, directly or indirectly, less than 50%



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of the voting power of the surviving entity, this Warrant shall, on the date of
such event, no longer be exercisable and become null and void. In the event of
a proposed transaction of the kind described above, the Company shall notify
the holder of the Warrant at least fifteen (15) days prior to the consummation
of such event or transaction.

                  4. Method of Exercise. While this Warrant remains outstanding
and exercisable in accordance with Section 3 above, the Holder may exercise, in
whole or in part, the purchase rights evidenced hereby. Such exercise shall be
effected by:

                           (a) the surrender of the Warrant, together with a
duly executed copy of the form of Notice of Election attached hereto, to the
Secretary of the Company at its principal offices; and

                           (b) the payment to the Company of an amount equal to
the aggregate Exercise Price for the number of Shares being purchased.

                  5. Net Exercise. In lieu of exercising this Warrant pursuant
to Section 4, the Holder may elect to receive, without the payment by the
Holder of any additional consideration, shares of Preferred Stock equal to the
value of this Warrant (or the portion thereof being canceled) by surrender of
this Warrant at the principal office of the Company together with notice of
such election, in which event the Company shall issue to the holder hereof a
number of shares of Preferred Stock computed using the following formula:

                                            Y(A-B)
                                            ------
                                    X=         A

            Where X = The number of shares of Preferred Stock to be issued to
                      the Holder pursuant to this net exercise;

                  Y = The number of Shares in respect of which the net issue
                      election is made:

                  A = The fair market value of one share of the Preferred Stock
                      at the time the net issue election is made;

                  B = The Exercise Price (as adjusted to the date of the net
                      issuance).

For purposes of this Section 5, the fair market value of one share of Preferred
Stock (or, Common Stock to the extent all such Preferred Stock has been
converted into the Company's Common Stock) as of a particular date shall be
determined in good faith by the Board of Directors of the Company; provided,
that, (i) if the Warrant is being exercised upon the closing of the Company's
first underwritten public offering pursuant to an effective registration
statement under the Securities Act of 1933, as amended, the value will be the
initial "Price to Public" of one share of such Preferred Stock (or Common Stock
issuable upon conversion of such Preferred Stock) specified in the final
prospectus with respect to such offering and (ii) if there is a public trading
market for the Company's Preferred Stock (or Common Stock) the value will be
the closing price of such shares on the day before the date of exercise.



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                  6. Certificates for Shares. Upon the exercise of the purchase
rights evidenced by this Warrant, one or more certificates for the number of
Shares so purchased shall be issued as soon as practicable thereafter (with
appropriate restrictive legends, if applicable), and in any event within thirty
(30) days of the delivery of the subscription notice.

                  7. Issuance of Shares. The Company covenants that the Shares,
when issued pursuant to the exercise of this Warrant, will be duly and validly
issued, fully paid and nonassessable and free from all taxes, liens, and
charges with respect to the issuance thereof.

                  8. Adjustment of Exercise Price and Number of Shares. The
number of and kind of securities purchasable upon exercise of this Warrant and
the Exercise Price shall be subject to adjustment from time to time as follows:

                     (a) Subdivisions, Combinations and Other Issuances. If the
Company shall at any time prior to the expiration of this Warrant subdivide its
Preferred Stock, by split-up or otherwise, or combine its Preferred Stock, or
issue additional shares of its Preferred Stock as a dividend with respect to
any shares of its Preferred Stock, the number of Shares issuable on-the
exercise of this Warrant shall forthwith be proportionately increased in the
case of a subdivision or stock dividend, or proportionately decreased in the
case of a combination. Appropriate adjustments shall also be made to the
purchase price payable per share, but the aggregate purchase price payable for
the total number of Shares purchasable under this Warrant (as adjusted) shall
remain the same. Any adjustment under this Section 8(a) shall become effective
at the close of business on the date the subdivision or combination becomes
effective, or as of the record date of such dividend, or in the event that no
record date is fixed, upon the making of such dividend.

                     (b) Reclassification, Reorganization and Consolidation. In
case of any reclassification, capital reorganization, or change in the
Preferred Stock of the Company (other than as a result of a subdivision,
combination, or stock dividend provided for in Section 8(a) above), then, as a
condition of such reclassification, reorganization, or change, lawful provision
shall be made, and duly executed documents evidencing the same from the Company
or its successor shall be delivered to the Holder, so that the Holder shall
have the right at any time prior to the expiration of this Warrant to purchase,
at a total price equal to that payable upon the exercise of this Warrant, the
kind and amount of shares of stock and other securities and property receivable
in connection with such reclassification, reorganization, or change by a holder
of the same number of shares of Preferred Stock as were purchasable by the
Holder immediately prior to such reclassification, reorganization, or change.
In any such case appropriate provisions shall be made with respect to the
rights and interest of the Holder so that the provisions hereof shall
thereafter be, applicable with respect to any shares of stock or other
securities and property deliverable upon exercise hereof, and appropriate
adjustments shall be made to the purchase price per share payable hereunder,
provided the aggregate purchase price shall remain the same.

                     (c) Notice of Adjustment. When any adjustment is required
to be made in the number or kind of shares purchasable upon exercise of the
Warrant, or in the Warrant Price, the Company shall promptly notify the holder
of such event and of the number of



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shares of Preferred Stock or other securities or property thereafter
purchasable upon exercise of this Warrant.

                  9. No Fractional Shares or Scrip. No fractional shares or
scrip representing fractional shares shall be issued upon the exercise of this
Warrant, but in lieu of such fractional shares the Company shall make a cash
payment therefor on the basis of the Exercise Price then in effect.

                  10. No Stockholder Rights. Prior to exercise of this Warrant,
the Holder shall not be entitled to any rights of a stockholder with respect to
the Shares, including (without limitation) the right to vote such Shares,
receive dividends or other distributions thereon, exercise preemptive rights or
be notified of stockholder meetings, and such holder shall not be entitled to
any notice or other communication concerning the business or affairs of the
Company. However, nothing in this Section 10 shall limit the right of the
Holder to be provided the Notices required under this Warrant or the Purchase
Agreement.

                  11. Transfers of Warrant. Subject to compliance with
applicable federal and state securities laws, this Warrant and all rights
hereunder are transferable in whole by the Holder to any person or entity upon
written notice to the Company. The transfer shall be recorded on the books of
the Company upon the surrender of this Warrant, properly endorsed, to the
Company at its principal offices, and the payment to the Company of all
transfer taxes and other governmental charges imposed on such transfer.

                  12. Successors and Assigns. The terms and provisions of this
Warrant and the Purchase Agreement shall inure to the benefit of, and be
binding upon, the Company and the Holders hereof and their respective
successors and assigns.

                  13. Amendments and Waivers. Any term of this Warrant may be
amended and the observance of any term of this Warrant may be waived (either
generally or in a particular instance and either retroactively or
prospectively), with the written consent of the Company and the holders of more
than 50% of shares of Preferred Stock issued or issuable upon exercise of
Warrants issued pursuant to the Purchase Agreement that are then outstanding.
Any waiver or amendment effected in accordance with this Section shall be
binding upon each holder of any Shares purchased under this Warrant at the time
outstanding (including securities into which such Shares have been converted),
each future holder of all such Shares, and the Company.

                  14. Effect of Amendment or Waiver. The Holder acknowledges
that by the operation of Section 13 hereof, the holders of more than 50% of
shares of Preferred Stock issued or issuable upon exercise of Warrants issued
pursuant to the Purchase Agreement will have the right and power to diminish or
eliminate all rights of such holder under this Warrant or under the Purchase
Agreement.

                  15. Notices. All notices required under this Warrant and
shall be deemed to have been given or made for all purposes (i) upon personal
delivery, (ii) upon confirmation receipt that the communication was
successfully sent to the applicable number if sent by facsimile; (iii) one day
after being sent, when sent by professional overnight courier service, or





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(iv) five days after posting when sent by registered or certified mail. Notices
to the Company shall be sent to the principal office of the Company (or at such
other place as the Company shall notify the Holder hereof in writing). Notices
to the Holder shall be sent to the address of the Holder on the books of the
Company (or at such other place as the Holder shall notify the Company hereof
in writing).

                  16. Attorneys' Fees. If any action of law or equity is
necessary to enforce or interpret the terms of this Warrant, the prevailing
party shall be entitled to its reasonable attorneys' fees, costs and
disbursements in addition to any other relief to which it may be entitled.

                  17. Captions. The section and subsection headings of this
Warrant are inserted for convenience only and shall not constitute a part of
this Warrant in construing or interpreting any provision hereof.

                  18. Governing Law. This Warrant shall be governed by the laws
of the State of Texas as applied to agreements among Texas residents made and
to be performed entirely within the State of Texas.



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                  IN WITNESS WHEREOF, the Company caused this Warrant to be
executed by an officer thereunto duly authorized.

                                     ODYSSEY HEALTHCARE, INC.



                                     By:
                                          -------------------------------------

                                     Name:
                                           ------------------------------------

                                     Title:
                                            -----------------------------------


<PAGE>   7
                               NOTICE OF EXERCISE


To: ODYSSEY HEALTHCARE, INC.

                  The undersigned hereby elects to [check applicable
subsection]:

-----------       (a)  Purchase _______________ shares of Series B Convertible
                       Preferred Stock of Odyssey HealthCare, Inc., pursuant to
                       the terms of the attached Warrant and payment of the
                       Exercise Price per share required under such Warrant
                       accompanies this notice;

                  OR

-----------       (b)  Exercise the attached Warrant for [all of the shares]
                       [_______ of the shares] [cross out inapplicable phrase]
                       purchasable under the Warrant pursuant to the net
                       exercise provisions of Section 5 of such Warrant.


                  The undersigned hereby represents and warrants that the
undersigned is acquiring such shares for its own account for investment
purposes only, and not for resale or with a view to distribution of such shares
or any part thereof.


                                 WARRANTHOLDER:


                                 ----------------------------------------------


                                 By:
                                     ------------------------------------------
                                             [NAME]

                                 Address:
                                          -------------------------------------

                                          -------------------------------------

Date:
       ------------------


Name in which shares should be registered:

-----------------------------------------
<PAGE>   8



                            LIST OF WARRANT HOLDERS

<TABLE>
<CAPTION>
                                                                             NUMBER OF
                HOLDER NAME                                     DATE           SHARES
                -----------                                     ----         ---------
<S>                                                            <C>           <C>
 1  Three Arch Partners, L.P.                                  5/22/98        25,512
 2  Three Arch Associates, L.P.                                5/22/98         5,739
 3  Weiss, Peck & Greer Venture Associates III, L.P.           5/22/98        14,011
 4  WPG Enterprise Fund II, L.P.                               5/22/98        16,850
 5  Oak Investment Partners VI                                 5/22/98        29,727
 6  Oak VI Affiliates                                          5/22/98           693
 7  Highland Capital Partners III Limited Partnership          5/22/98        13,315
 8  Highland Entrepreneurs Fund III Limited Partnership        5/22/98           554
 9  Collinson Home Venture Partners, Inc.                      5/22/98           866
10  David L. Steffy                                            5/22/98        12,726
                                                                             -------
    Total outstanding                                                        119,993
</TABLE>