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                                                                     EXHIBIT 4.3
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                        THE MERIDIAN RESOURCE CORPORATION



                                       AND



                       AMERICAN STOCK TRANSFER & TRUST CO.



                                  RIGHTS AGENT


                               AMENDMENT NO. 1 TO


                                RIGHTS AGREEMENT



                          DATED AS OF JANUARY 29, 2001



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                                 AMENDMENT NO. 1
                               TO RIGHTS AGREEMENT

         This Amendment No. 1 dated as of January 29, 2001 (this "Amendment") to
the Rights Agreement (the "Agreement") dated as of May 5, 1999, between The
Meridian Resource Corporation, a Texas corporation (the "Company"), and American
Stock Transfer & Trust Co. (the "Rights Agent").

         The Board of Directors of the Company has authorized various amendments
to the Agreement.

         Accordingly, in consideration of the premises and the mutual agreements
herein set forth, the parties hereby agree as follows:

         SECTION 1. CERTAIN DEFINITIONS. For purposes of this Amendment,
capitalized terms not otherwise defined in this Amendment shall have the
meanings assigned to them in the Agreement:

         SECTION 2. AMENDMENT TO THE DEFINITION OF "ACQUIRING PERSON". The
definition of "Acquiring Person" contained in Section 1(a) of the Agreement is
hereby amended and restated in its entirety as follows:

         "(a) "Acquiring Person" shall mean any Person (as such term is
hereinafter defined) who or which, together with all Affiliates and Associates
(as such terms are hereinafter defined) of such Person, shall be the Beneficial
Owner (as such term is hereinafter defined) of 15% or more of the Common Shares
then outstanding, but shall not include (i) the Company, (ii) any Subsidiary (as
such term is hereinafter defined) of the Company, (iii) any employee benefit
plan of the Company or of any Subsidiary of the Company or (iv) any Person
holding Common Shares for or pursuant to the terms of any such plan to the
extent, and only to the extent, of the Common Shares so held. Notwithstanding
the foregoing, no Person shall become an "Acquiring Person" as the result of an
acquisition of Common Shares by the Company which, by reducing the number of
shares outstanding, increases the proportionate number of shares beneficially
owned by such Person to 15% or more of the Common Shares then outstanding;
provided, however, that if a Person becomes the Beneficial Owner of 15% or more
of the Common Shares then outstanding by reason of share acquisitions by the
Company and shall, after such share acquisitions by the Company, become the
Beneficial Owner of any additional Common Shares, then such Person shall be
deemed to be an "Acquiring Person". Notwithstanding the foregoing, if the Board
of Directors of the Company determines in good faith that a Person who would
otherwise be an "Acquiring Person", as defined pursuant to the foregoing
provisions of this Section 1(a), has become such inadvertently, and such Person
divests as promptly as practicable a sufficient number of Common Shares so that
such Person would no longer be an "Acquiring Person", as defined pursuant to the
foregoing provisions of this Section 1(a), then such Person shall not be deemed
to be an "Acquiring Person" for any purposes of this Agreement."
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         SECTION 3. REMOVAL OF CERTAIN DEFINITIONS. Sections 1(n), 1(o) and 1(p)
of the Agreement are deleted in their entirety and Section 1(q) is renumbered to
be Section 1(n).

         SECTION 4. AMENDMENT TO SECTION 13(b). Section 13(b) of the Agreement
is hereby amended and restated in its entirety as follows:

                  "(b) "Principal Party" shall mean

                       (1) in the case of any transaction described in clause
                           (i) or (ii) of the first sentence of Section 13(a),
                           the Person that is the issuer of any securities into
                           which Common Shares are converted in such
                           transaction, and if no securities are so issued, the
                           Person that is the other party to the transaction;
                           and

                       (2) in the case of any transaction described in clause
                           (iii) of the first sentence in Section 13(a), the
                           Person that is the party receiving the greatest
                           portion of the assets or earning power transferred
                           pursuant to such transaction or transactions;

provided, however, that in any such case, (1) if the securities of such Person
are not at such time or have not been continuously over the preceding 12-month
period registered under Section 12 of the Exchange Act, and such Person is a
direct or indirect Subsidiary of another Person the securities of which are and
have been so registered, "Principal Party" shall mean such other Person; (2) in
case such Person is a Subsidiary, directly or indirectly, of more than one other
Person, the securities of two or more of which are and have been so registered,
"Principal Party" shall mean whichever of such other Persons is the issuer of
the securities so registered having the greatest aggregate market value; and (3)
in case such Person is owned, directly or indirectly, by a joint venture formed
by two or more other Persons that are not owned, directly or indirectly, by the
same Person, the rules set forth in (1) and (2) above shall apply to each of the
chains of ownership having an interest in such joint venture as if such Person
were a "Subsidiary" of both or all of such other Persons and the Principal
Parties in each such chain shall bear the obligations set forth in this Section
13 in the same ratio as their direct and indirect interests in such Person bear
to the total of such interests."

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         IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
duly executed and attested, all as of the day and year first above written.

                                            THE MERIDIAN RESOURCE CORPORATION



                                                 /s/ Joseph A. Reeves, Jr.
                                            ------------------------------------
                                                     Joseph A. Reeves, Jr.
                                                     Chairman of the Board
                                                  and Chief Executive Officer


                                            AMERICAN STOCK TRANSFER & TRUST CO.



                                            By:   /s/ Herbert J. Lemmer
                                               ---------------------------------
                                            Name:     Herbert J. Lemmer
                                                 -------------------------------
                                            Title:    Vice President
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