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                                                                     EXHIBIT 4.1

                       FIRST AMENDMENT TO RIGHTS AGREEMENT

      THIS AGREEMENT (the "Amendment"), dated as of the 17th day of October,
2004, between Select Medical Corporation, a Delaware corporation (the
"Company"), and Mellon Investor Services LLC, a New Jersey limited liability
company (the "Rights Agent"), constitutes the First Amendment to the Rights
Agreement, dated as of September 17, 2001, between the Company and the Rights
Agent (as amended and in effect from time to time, the "Rights Agreement").
Terms not otherwise defined herein shall have the meanings assigned to such
terms in the Rights Agreement.

                                   WITNESSETH

      WHEREAS, pursuant to Section 27 of the Rights Agreement, the Board of
Directors of the Company has approved an amendment of certain provisions of the
Rights Agreement as set forth below;

      NOW, THEREFORE, the Rights Agreement is hereby amended as follows:

1.    Amendments to Section 1.

      (a)   Additional Definitions. Section 1 of the Rights Agreement is hereby
amended by inserting the following subsections at the end of such Section 1:

            "(oo) "Merger" shall have the meaning set forth in the Merger
      Agreement."

            "(pp) "Merger Agreement" shall mean the Agreement and Plan of Merger
      dated as of October 17, 2004 among EGL Holding Company, EGL Acquisition
      Corp. and the Company, as amended from time to time."

            "(qq) "Rollover Stockholders" shall have the meaning set forth in
      the Merger Agreement."

            "(rr) "Sponsor" means Welsh, Carson, Anderson & Stowe IX, L.P., a
      Delaware limited partnership."

      (b)   Amendment to Definition of "Acquiring Person." Section 1(a) of the
Rights Agreement is amended by inserting the following sentence at the end of
such Section 1(a):

            "Notwithstanding anything in this Section 1(a) to the contrary, none
            of (i) the Sponsor, EGL Holding Company, EGL Acquisition Corp., (ii)
            the Rollover Stockholders and (iii) the respective Subsidiaries,
            Associates, Affiliates, spouses, general partners and limited
            partners of the Persons described in clauses (i) and (ii) (the
            Persons described in clauses (i), (ii) and (iii) collectively the
            "Covered Persons") either individually, collectively or in any
            combination shall be or be deemed to be an Acquiring Person by
            virtue of or as a result of (A) any agreements, arrangements or
            understandings among all or any of the Covered Persons in connection
            with the Merger Agreement, the transactions contemplated
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            thereby or the ownership of EGL Holding Company, (B) the execution
            of the Merger Agreement, (C) the acquisition of any shares of
            capital stock of the Company pursuant to the Merger Agreement or the
            consummation of the Merger, or (D) the consummation of the other
            transactions contemplated by the Merger Agreement (the transactions
            described in clauses (A), (B), (C) and (D), the "Exempted
            Transactions")."

      (c)   Amendment to Definition of "Beneficial Owner." Section 1(d) of the
Rights Agreement is amended by inserting the following sentence at the end of
such Section 1(d):

            "Notwithstanding anything in this Section 1(d) to the contrary, none
            of the Covered Persons, either individually, collectively or in any
            combination, shall be deemed to be a Beneficial Owner of or to
            beneficially own any securities beneficially owned, directly or
            indirectly, by any other Covered Person solely by virtue of or as a
            result of any Exempted Transaction."

      (d)   Amendment to Definition of "Stock Acquisition Date." Section 1(ii)
of the Rights Agreement is amended by inserting the following sentence at the
end of such Section 1(ii):

            "Notwithstanding anything in this Section 1(ii) to the contrary, a
            Stock Acquisition Date shall not be deemed to have occurred by
            virtue of or as a result of the public announcement of any Exempted
            Transaction."

2.    Amendment to Section 3(a). Section 3(a) of the Rights Agreement is hereby
amended by inserting the following sentence at the end of such Section 3(a):

            "Notwithstanding anything in this Agreement to the contrary, a
            Distribution Date shall not be deemed to have occurred by virtue of
            or as a result of any Exempted Transaction."

3.    Amendment to Section 7(a). Section 7(a) of the Rights Agreement is hereby
amended to read in its entirety as follows:

            "(a) Subject to Section 7(e), the registered holder of any Right
            Certificate may exercise the Rights evidenced thereby (except as
            otherwise provided herein including, without limitation, the
            restrictions on exercisability set forth in Section 9(c), Section
            11(a)(iii) and Section 23(a)), in whole or in part at any time after
            the Distribution Date, upon surrender of the Right Certificate, with
            the form of election to purchase and the certificate on the reverse
            side thereof duly executed, to the Rights Agent at the office of the
            Rights Agent designated for such purpose, together with payment of
            the aggregate Purchase Price with respect to the total number of one
            one-hundredths of a share of Preferred Stock (or other securities,
            cash or other assets, as the case may be) as to which such
            surrendered Rights are then exercisable, at or prior to the earliest
            of (i) the Close of Business on the tenth anniversary hereof (the
            "Final Expiration Date"), (ii) immediately prior to the effective
            time of the Merger, but only if such effective time shall occur,
            (iii) the

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            time at which the Rights are redeemed as provided in Section 23 (the
            "Redemption Date"), or (iv) the time at which such Rights are
            exchanged as provided in Section 24."

4.    Addition of Section 35. The Rights Agreement is hereby amended by adding
the following Section 35 to the end of the Rights Agreement:

            "Section 35. Termination. Immediately prior to the effective time of
            the Merger, but only if such effective time shall occur, (a) the
            Rights Agreement shall be terminated and be without any further
            force or effect, (b) none of the parties to the Rights Agreement
            will have any rights, obligations or liabilities thereunder and (c)
            the holders of the Rights shall not be entitled to any benefits,
            rights or other interests under the Rights Agreement, including,
            without limitation, the right to purchase or otherwise acquire
            Preferred Stock or any other securities of the Company.
            Notwithstanding the foregoing, Section 18 hereof shall survive the
            termination of the Rights Agreement. The Company will notify in
            writing the Rights Agent of the effective time of the Merger. The
            Rights Agent will not be deemed to have knowledge of the effective
            time of the Merger unless and until it has received such written
            notice."

5.    Effectiveness. This Amendment shall be deemed effective as of the date
first written above, as if executed on such date. Except as amended hereby, the
Rights Agreement shall remain in full force and effect and shall be otherwise
unaffected hereby.

6.    Miscellaneous. This Amendment shall be deemed to be a contract made under
the laws of the State of Delaware and for all purposes shall be governed by and
construed in accordance with the laws of such State applicable to contracts to
be made and performed entirely within such State; provided, however, that all
provisions regarding the rights, duties and obligations of the Rights Agent
shall be governed by and construed in accordance with the laws of the State of
New York applicable to contracts made and to be performed entirely within such
State. This Amendment may be executed in any number of counterparts and each of
such counterparts shall for all purposes be deemed to be an original, an all
such counterparts shall together constitute but one and the same instrument. If
any term, provision, covenant or restriction of this Amendment is held by a
court of competent jurisdiction or other authority to be invalid, illegal or
unenforceable, the remainder of the terms, provisions, covenants and
restrictions of this Amendment shall remain in full force and effect and shall
in no way be affected, impaired or invalidated.

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      IN WITNESS WHEREOF, the parties hereto have caused this First Amendment to
Rights Agreement to be duly executed as of the date first above written.

                                             SELECT MEDICAL CORPORATION

                                             By: /s/ Michael E. Tarvin
                                                 ------------------------------
                                                 Name:  Michael E. Tarvin
                                                 Title: Senior Vice President

                                             MELLON INVESTOR SERVICES LLC,
                                             as Rights Agent

                                             By: /s/ Linda Fuhrer
                                                 -------------------------------
                                                 Name:  Linda Fuhrer
                                                 Title: Assistant Vice President

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