Document:

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                                                                     EXHIBIT 4.2

                          REGISTRATION RIGHTS AGREEMENT

         REGISTRATION RIGHTS AGREEMENT, dated January 29, 2001 by and between
The Meridian Resource Corporation, a Texas corporation (the "Company"), and
Shell Louisiana Onshore Properties Inc., a Delaware corporation ("Security
Holder").

                              W I T N E S S E T H:

         WHEREAS, the Company and Security Holder have entered into an Option
and Standstill Agreement dated July 17, 2000 (the "Option Agreement"), which
provides, among other things, for the execution of this Agreement;

         NOW THEREFORE, in consideration of the mutual covenants and agreements
set forth herein and in the Option Agreement the parties hereto agree as
follows:

         Section 1. Definitions. The terms defined in this Section 1, whenever
used in this Agreement, shall, unless the context otherwise requires, have the
respective meanings hereinafter specified. Terms not defined in this Agreement,
and defined in the Option Agreement have the meanings assigned them in the
Option Agreement.

         "Agreement" shall mean this Registration Rights Agreement.

         "Commission" shall mean the United States Securities and Exchange
Commission.

         "Common Stock" shall mean the Company's authorized Common Stock, par
value $0.01 per share.

         "Company" shall mean The Meridian Resource Corporation, a Texas
corporation, and any successor corporation by merger, consolidation or otherwise
and any parent corporation resulting from the merger or consolidation of the
Company with or into a subsidiary of another corporation.

         "Eligible Stock" means the 7,082,030 shares of Common Stock issued in
the name of Security Holder, representing all equity shares of the Company
beneficially owned by Security Holder after giving effect to the transactions
contemplated by the Option Agreement.

         "E&P Company" shall mean a Person that, directly or indirectly, has as
one of its material businesses the exploration, development or production of
crude oil or natural gas.

         "Exchange Act" shall mean the Securities Exchange Act of 1934, and the
rules and regulations of the Commission thereunder, all as the same shall be in
effect at the time.

         "Permitted Transferee" shall mean any Person to which Security Holder
transfers all, but not a portion, of the Registrable Securities.

         "Person" shall mean an individual, a corporation, a partnership, a
trust, an unincorporated organization or a government or any agency or political
subdivision thereof.
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         "Public Offering" shall mean a firm commitment underwritten public
offering pursuant to a registration statement under the Securities Act.

         "Registrable Securities" shall mean the Eligible Stock and any shares
of Common Stock issued or issuable in respect of such shares by way of a stock
dividend or stock split or in connection with a combination or subdivision of
shares, reclassification, recapitalization, merger, consolidation or other
reorganization of the Company. As to any particular Registrable Securities, such
securities shall cease to be Registrable Securities when (a) a registration
statement with respect to the sale of such securities shall have become
effective under the Securities Act and such securities shall have been disposed
of in accordance with such registration statement, (b) they shall have been
distributed to the public pursuant to Rule 144 (or any successor provision)
under the Securities Act, (c) disposition of them shall not require registration
or qualification of them under the Securities Act or any similar law then in
force or compliance with any rule or regulation under the Securities Act or
similar law, other than compliance with any holding period required by such rule
or regulation, (d) they shall have been otherwise transferred to any Person
other than a Permitted Transferee or (e) they shall have ceased to be
outstanding.

         "Registration" shall mean the registration under the Securities Act of
Registrable Securities pursuant to either Section 2.A hereof or 2.B hereof.

         "Registration Statement" shall mean a registration statement filed
under the Securities Act or a similar document filed pursuant to any other
statute then in effect corresponding to the Securities Act.

         "Securities Act" shall mean the Securities Act of 1933, and the rules
and regulations of the Commission thereunder, all as the same shall be in effect
at the time.

         "Security Holder" shall mean Shell Louisiana Onshore Properties Inc., a
Delaware corporation, its permitted assigns, or any affiliate thereof holding
Common Stock or any successor corporation to any of the foregoing by merger or
consolidation or otherwise.

Section 2. Registration Rights.

         A. Demand Registrations. Subject to the provisions of Section 5 in the
event of assignment of this Agreement, if the Company shall receive a written
request from Security Holder requesting that the Company file a Registration
Statement relating to Registrable Securities, the Company will as promptly as
practicable prepare and file a Registration Statement and use reasonable best
efforts to cause the Registration Statement to become effective; subject,
however, to the following provisions:

                  (1) the Company shall be required to file no more than an
         aggregate of two Registration Statements on behalf of Security Holder
         (or Permitted Transferee in the event of an assignment of this
         Agreement) pursuant to this Subsection A; (1)

                  (2) the Company shall not be obligated (i) to file a requested
         Registration in the event that the aggregate number of Registrable
         Securities to be included in such requested Registration is less than
         500,000 shares of the issued and outstanding Common Stock; or (ii) to
         prepare or file such Registration Statement or an amendment or
         supplement

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         thereto, and may suspend sales, at any time when the Company reasonably
         determines (by action of the Company's Board of Directors or an officer
         duly authorized by the Board of Directors to make such decision) that
         the filing thereof at the time requested, or the offering of
         Registrable Securities pursuant thereto, would materially and adversely
         affect a pending or proposed offering of securities of the Company, an
         acquisition, merger, recapitalization, consolidation, reorganization or
         similar transaction relating to the Company or negotiations,
         discussions or pending proposals with respect thereto or require
         premature disclosure of information not otherwise required to be
         disclosed to the potential detriment of the Company; provided, however,
         that such period of sale or distribution shall resume after any such
         suspension for a number of days necessary to keep such Registration
         effective for permitted sales thereunder for a term of 90 days. The
         filing of a Registration Statement, or any amendment or supplement
         thereto, by the Company may not be deferred, and the sale and
         distribution of shares may not be suspended, in each case pursuant to
         the foregoing provisions, for more than 60 days after the abandonment
         or consummation (or the completion of the distribution of securities in
         the case of a public offering) of any of the proposals or transactions
         described therein or, in any event, for more than 120 days during any
         one year;

                  (3) a Registration Statement filed pursuant to a request of
         Security Holder shall first include all Registrable Securities
         requested to be included by Security Holder and, only after such
         inclusion, may, include securities of the Company being sold for the
         account of the Company; provided, however, that securities to be
         offered on behalf of the Company will be included in such Registration
         Statement only to the extent that, in the reasonable opinion of the
         managing underwriter for the Public Offering of Registrable Securities
         on behalf of Security Holder, such inclusion will not materially
         adversely affect the distribution of Registrable Securities on behalf
         of Security Holder;

                  (4) the selection of an underwriter for a Public Offering of
         Registrable Securities by Security Holder shall be subject to the
         approval of the Company, which shall not be unreasonably withheld;

                  (5) for purposes of paragraph (1) of this Subsection A, if a
         requested Registration Statement is filed and the Company otherwise
         complies with its obligations hereunder, but the Registration Statement
         is withdrawn by Security Holder due to a delay in the offering
         requested by the Company for a period of more than 15 business days
         pursuant to paragraph (2) of this Subsection A, then no requested
         Registration Statement shall be deemed to have been filed; and

                  (6) no Other Holder (as defined below) shall be entitled to
         include securities or piggyback in any Registration demanded by
         Security Holder.

         B. Incidental/"Piggy-back" Registrations. If the Company at any time
proposes to file a Registration Statement (other than a Registration Statement
filed pursuant to Subsection A of this Section 2) under the Securities Act
relating to a Public Offering of Common Stock to be sold for cash that would
permit the registration of Registrable Securities, it will give Security Holder
as much advance notice, in writing, as is reasonably practicable under the
circumstances, but in any event not less than five days, before the filing with
the Commission of such Registration Statement,

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which notice shall set forth the securities proposed to be registered. The
notice shall offer to include in such filing such amount of Registrable
Securities as Security Holder may request. If Security Holder wishes to have
Registrable Securities registered for sale in the Public Offering pursuant to
this Subsection B, it shall advise the Company in writing within 20 days after
the date of receipt of such offer from the Company (or such shorter period, but
in any event not less than five days, as the Company shall specify in its notice
to Security Holder), setting forth the amount of Registrable Securities for
which registration is requested. If the managing underwriter of the proposed
Public Offering of Common Stock by the Company shall advise the Company in
writing that, in the reasonable opinion of the managing underwriter, the
distribution of the Registrable Securities requested by Security Holder to be
included in the Registration Statement concurrently with securities being
registered for sale by the Company would materially adversely affect the
distribution of such securities by the Company and Security Holder, then the
Company shall so advise Security Holder and the number of securities that are
entitled to be included in the registration and underwriting shall be allocated
as follows: (i) in the event a Registration Statement is being filed in
connection with the exercise of registration rights by a security holder other
than Security Holder (an "Other Holder"), all of any Other Holder's shares of
Common Stock shall be included in the registration and the remaining number of
securities that are entitled to be included in the registration shall be
allocated (A) 80% to the Company and any other shareholders (not including the
Other Holder or Security Holder) whose shares are to be included in such
Registration Statement and (B) 20% to Security Holder, and (ii) in the event the
registration is not being filed in connection with the exercise of registration
rights of any Other Holder (A) 80% to the Company and any other shareholders
(not including Security Holder) whose shares are to be included in such
Registration Statement and (B) 20% to Security Holder. If any Person does not
agree to the terms of any such underwriting, such Person shall be excluded
therefrom by written notice from the Company or the underwriter.

         Nothing contained in this Subsection B shall, however, limit the
Company's right to cancel, postpone or withdraw any such registration proposed
by the Company for any reason.

         Any obligation of the Company to effect a Registration pursuant to this
Subsection B shall be conditioned upon Security Holder entering into an
underwriting agreement with the Company and the managing underwriters of the
registered offering of the type described in paragraph (10) of Subsection C of
this Section 2.

         C. Registration Procedures. If the Company is required by the
provisions of Subsection A or Subsection B of this Section 2 to effect the
Registration of any of the Registrable Securities under the Securities Act, the
Company will, as soon as is reasonably practicable:

                  (1) Prepare and file with the Commission a Registration
         Statement with respect to such securities and use its reasonable best
         efforts to cause such Registration Statement to become and, subject to
         paragraph (2) of this Subsection C, remain effective.

                  (2) Keep such Registration effective, and the prospectus used
         in connection therewith current, for a period of 90 days or until
         Security Holder has completed the distribution described in the
         Registration Statement relating thereto, whichever first occurs (the
         "Selling Period"); provided, however, that (a) the Selling Period shall
         be extended for a period of time equal to any period that Security
         Holder refrains from selling

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         any securities included in such registration pursuant to a suspension
         under paragraph (2) of Subsection A of this Section 2.

                  (3) Prepare and file with the Commission such amendments and
         supplements to such Registration Statement and the prospectus used in
         connection therewith as may be necessary to keep such Registration
         Statement effective and such prospectus current in compliance with
         Section 10 of the Securities Act, and to comply with the provisions of
         the Securities Act with respect to the sale or other disposition of all
         Common Stock covered by such Registration Statement; provided, however,
         that the Company shall have no obligation under this paragraph (3)
         after the period required by paragraph (2) of this Subsection C has
         lapsed.

                  (4) Furnish to Security Holder such number of copies of such
         Registration Statement and of each amendment and supplement thereto (in
         each case including all exhibits), such number of copies of the
         prospectus included in such Registration Statement (including each
         preliminary prospectus, summary prospectus and prospectus supplement),
         in conformity with the requirements of the Securities Act, and such
         other documents, as Security Holder may reasonably require in order to
         facilitate the public offering, sale or other disposition of the
         Registrable Securities owned by Security Holder.

                  (5) Use reasonable best efforts to register or qualify the
         Common Stock covered by such Registration Statement under such other
         securities or blue sky laws of jurisdictions in the United States of
         America as Security Holder shall reasonably request (excluding however
         any jurisdiction in which the filing would subject the Company to
         additional tax liability, and any jurisdiction in which the Company
         would be required to execute a general consent to service of process in
         effecting such registration or qualification, which consent would not
         be required but for this paragraph (5)), and do such other acts and
         things as may be required to enable Security Holder to consummate the
         public sale or other disposition in such jurisdictions of the
         Registrable Securities owned by Security Holder.

                  (6) Otherwise use reasonable best efforts to comply with all
         applicable rules and regulations of the Commission, and make available
         to its security holders, as soon as reasonably practicable, an earnings
         statement that satisfies the provisions of Section 11(a) of the
         Securities Act.

                  (7) Immediately notify Security Holder at any time when a
         prospectus is required to be delivered under the Securities Act within
         the Selling Period referred to in paragraph (2) of this Subsection C,
         of the Company becoming aware that the prospectus included in the
         Registration Statement, or as such prospectus may be amended or
         supplemented, includes an untrue statement of a material fact or omits
         to state any material fact required to be stated therein or necessary
         in order to make the statements therein not misleading in light of the
         circumstances then existing, and at the request of Security Holder to
         promptly prepare and furnish to Security Holder a number of copies of
         an amended or supplemental prospectus as may be necessary so that, as
         thereafter delivered to the purchasers of such Registrable Securities,
         such prospectus shall not include an untrue statement of a material
         fact or omit to state a material fact required to be stated therein or
         necessary in order to make the statements therein not misleading in the
         light of the circumstances then existing.

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         In the event the Company shall give any such notice, Security Holder
         shall immediately suspend use of the prospectus and the Selling Period
         shall be extended by the number of days during the period from and
         including the date of the giving of such notice to and including the
         date when Security Holder shall have received the copies of such
         supplemented or amended prospectus.

                  (8) In the event that the Company suspends use by Security
         Holder of a prospectus relating to an offering of Registrable
         Securities pursuant to a suspension under paragraph (2) of Subsection A
         of this Section 2, because the Company is conducting negotiations for a
         material business combination or due to pending material developments
         or events that have not yet been publicly disclosed and as to which the
         Company believes public disclosure will be prejudicial to the Company,
         the Company shall deliver notice in writing to the effect of the
         foregoing and, upon receipt of such notice, Security Holder shall not
         use the prospectus, and the Selling Period shall cease to run or will
         not commence, until Security Holder has received copies of the
         supplemented or amended prospectus provided for in paragraph (3) of
         this Subsection C, or until it is advised in writing by the Company
         that the prospectus may be used, and has received copies of any
         additional or supplemental filings that are incorporated or deemed
         incorporated by reference in such prospectus. The Company will use
         reasonable best efforts to ensure that the use of the prospectus may be
         resumed, and the Selling Period will commence, as promptly as is
         practicable and, in any event, promptly after the earlier of (x) public
         disclosure of such material business combination or pending material
         development or event sufficient to permit an affiliate of the Company
         to sell Common Stock or (y) in the judgment of the Company, public
         disclosure of such material business combination or material
         development or event would not be prejudicial to the Company.

                  (9) Use its reasonable best efforts to list such Registrable
         Securities on the primary securities exchange or other trading market
         on which the Common Stock is then listed, if such Registrable
         Securities are not already so listed and if such listing is then
         permitted under the rules of such exchange or other trading market, and
         to provide a transfer agent and registrar for such Registrable
         Securities covered by such Registration Statement not later than the
         effective date of such Registration Statement.

                  (10) Enter into such agreements (including an underwriting
         agreement in customary form and containing customary provisions
         relating to legal opinions and accountants' letters and customary
         representations and warranties and customary provisions for mutual
         indemnification and contribution between the Company and the
         underwriters for Security Holder) and take such other actions as
         Security Holder may reasonably request in order to expedite or
         facilitate the disposition of such Registrable Securities.

                  (11) Make available for inspection by Security Holder, by any
         underwriter participating in any disposition to be effected pursuant to
         such Registration Statement and by any attorney, accountant or other
         agent retained by Security Holder or any such underwriter, all
         customary financial and other records, customary corporate documents
         and properties of the Company, and cause all of the Company's officers,
         directors and employees to supply all customary information requested
         by Security Holder, such underwriter, attorney, accountant or agent, as
         is reasonably needed in connection with such Registration Statement;

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         provided such parties execute confidentiality agreements reasonably
         acceptable to the Company.

         Underwriting discounts and commissions attributable to securities
offered on behalf of Security Holder plus the fees and expenses of separate
counsel for Security Holder incurred in connection with effecting a Registration
pursuant to this Section 2 shall be borne by Security Holder. All other expenses
incurred in connection with the Registration Statement shall be borne by the
Company.

         It shall be a condition precedent to the obligation of the Company to
take any action pursuant to this Section 2 in respect of the Registrable
Securities that are to be registered at the request of Security Holder that
Security Holder shall furnish to the Company such information regarding the
securities held by it and the intended method of disposition thereof as the
Company shall reasonably request and as shall be required in connection with the
action taken by the Company.

         D. Indemnification.

                  (1) In the event of any Registration of any Registrable
         Securities under the Securities Act pursuant to this Section 2, the
         Company agrees to indemnify and hold harmless Security Holder, its
         directors, officers and employees, and each other Person, if any, who
         controls Security Holder within the meaning of Section 15 of the
         Securities Act, against any losses, claims, damages or liabilities,
         joint or several, to which Security Holder or any such director,
         officer, employee or controlling Person may become subject under the
         Securities Act or any other statute or at common law, insofar as such
         losses, claims, damages or liabilities (or actions in respect thereof)
         arise out of or are based upon (i) any alleged untrue statement of any
         material fact contained, on the effective date thereof, in any
         Registration Statement under which Registrable Securities were
         registered under the Securities Act at the request of Security Holder,
         any preliminary prospectus or final prospectus contained therein, or
         any amendment or supplement thereto, or (ii) any alleged omission to
         state therein a material fact required to be stated therein or
         necessary to make the statements therein not misleading, and shall
         reimburse Security Holder or such director, officer, employee or
         controlling Person for reasonable legal or any other expenses
         reasonably incurred by Security Holder or such director, officer,
         employee or controlling Person in connection with investigating or
         defending any such loss, claim, damage, liability or action; provided,
         however, that the Company shall not be liable in any such case to the
         extent that any such loss, claim, damage, liability or expense arises
         out of or is based upon any alleged untrue statement or alleged
         omission made in such Registration Statement, preliminary prospectus,
         prospectus, or amendment or supplement in reliance upon and in
         conformity with written information furnished to the Company by
         Security Holder in writing for use therein; and provided, further, that
         the Company shall not be liable in any such case to the extent that any
         such loss, claim, damage, liability or expense arises out of or is
         based upon an untrue statement or alleged untrue statement or omission
         or alleged omission in the prospectus if such untrue statement or
         alleged untrue statement or omission or alleged omission has been the
         subject of a notice given to Security Holder pursuant to paragraph (7)
         of Subsection C of this Section 2 if Security Holder after receipt of
         such notice and prior to the receipt of a corrected prospectus sold a
         Registrable Security to the Person asserting such loss, claim,

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         damage, liability or expense who purchased such Registrable Security
         that is the subject thereof from Security Holder. Such indemnity shall
         remain in full force and effect regardless of any investigation made by
         or on behalf of Security Holder or such director, officer, employee or
         participating Person or controlling Person, and shall survive the
         transfer of such securities by Security Holder.

                  (2) Security Holder agrees to indemnify and hold harmless the
         Company, its directors, officers and employees and each other Person,
         if any, who controls the Company within the meaning of Section 15 of
         the Securities Act against any losses, claims, damages or liabilities,
         joint or several, to which the Company or any such director, officer,
         employee or controlling Person may become subject under the Securities
         Act or any other statute or at common law, insofar as such losses,
         claims, damages or liabilities (or actions in respect thereof) arise
         out of or are based upon (i) any alleged untrue statement of any
         material fact contained, on the effective date thereof, in any
         Registration Statement under which Registrable Securities were
         registered under the Securities Act at the request of Security Holder,
         any preliminary prospectus or final prospectus contained therein, or
         any amendment or supplement thereto, or (ii) any alleged omission to
         state therein a material fact required to be stated therein or
         necessary to make the statements therein not misleading, in each case
         to the extent, but only to the extent, that such alleged untrue
         statement or alleged omission was made in such Registration Statement,
         preliminary prospectus, prospectus, amendment or supplement in reliance
         upon and in conformity with written information furnished to the
         Company in writing by Security Holder for use therein, and shall
         reimburse the Company or such director, officer, employee or
         controlling Person for any reasonable legal or any other expenses
         reasonably incurred by the Company or such director, officer, employee
         or controlling Person in connection with investigating or defending any
         such loss, claim, damage, liability or action.

                  (3) Promptly after receipt by an indemnified party hereunder
         of written notice of the commencement of any action or proceeding
         involving a claim referred to in the preceding paragraphs of this
         Subsection D, such indemnified party will, if a claim in respect
         thereof is to be made against an indemnifying party, give written
         notice to the latter of the commencement of such action; provided, that
         the failure of any indemnified party to give notice as provided herein
         shall not relieve the indemnifying party of its obligation under this
         Subsection D to the extent the indemnifying party is not materially
         prejudiced by such failure. In case any such action is brought against
         an indemnified party, the indemnified party shall permit the
         indemnifying party to assume the defense of such action or proceeding,
         provided that counsel for the indemnifying party, who shall conduct the
         defense of such action or proceeding, shall be approved by the
         indemnified party (whose approval shall not be unreasonably withheld)
         and the indemnified party may participate in such defense at such
         indemnified party's expense unless in the opinion of counsel to such
         indemnified party a conflict of interest between such indemnified and
         indemnifying parties may exist in respect of such claim that would
         prevent the indemnifying party's counsel from adequately representing
         both parties, in which event the indemnifying party shall pay the
         reasonable fees and expense of separate counsel for the indemnified
         party. No indemnifying party will consent to entry of any judgment or
         enter into any settlement that does not include as an unconditional
         term thereof the giving by the claimant or plaintiff to such
         indemnified party of a release from all liability in respect to such
         claim or litigation. The indemnifying party

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         shall not, in connection with any proceeding or related proceedings in
         the same jurisdiction, be liable for the fees and expenses of more than
         one separate firm for all indemnified parties. The indemnifying party
         shall not be liable for any settlement of any proceeding effected
         without its written consent.

                  (4) Indemnification similar to that specified in the preceding
         paragraphs of this Subsection D shall be given by the Company and
         Security Holder (with such modifications as shall be appropriate) with
         respect to liability related to any required registration or other
         qualification of Registrable Securities under any Federal or state law
         or regulation of governmental authority other than the Securities Act.

                  (5) If the indemnification provided for in this Subsection D
         is unavailable or insufficient to hold harmless an indemnified party
         under paragraphs (1) or (2) above, then the indemnifying party shall
         contribute to the amount paid or payable by such indemnified party as a
         result of the losses, claims, damages or liabilities referred to in
         paragraphs (1) or (2) above, in such proportion as is appropriate to
         reflect the relative fault of the Company on the one hand and Security
         Holder on the other in connection with the statements or omissions that
         resulted in such losses, claims, damages or liabilities, as well as any
         other relevant equity considerations. The relative fault shall be
         determined by reference to, among other things, whether the untrue or
         alleged untrue statement of a material fact or the omission or alleged
         omission to state a material fact relates to information supplied by
         the Company or Security Holder and the parties' relative intent,
         knowledge, access to information and opportunity to correct or prevent
         such untrue statement or omission. The Company and Security Holder
         agree that it would not be just and equitable if contributions pursuant
         to this paragraph (5) were to be determined by pro rata allocation or
         by any other method of allocation that does not take account of the
         equitable considerations referred to in the first sentence of this
         paragraph (5). The amount paid by an indemnified party as a result of
         the losses, claims, damages or liabilities referred to in the first
         sentence of this paragraph (5) shall be deemed to include any legal or
         other expenses reasonably incurred by such indemnified party in
         connection with investigating or defending any action or claim (which
         shall be limited as provided in paragraph (3) above if the indemnifying
         party has assumed the defense of any such action in accordance with the
         provisions thereof) that is the subject of this paragraph (5).
         Notwithstanding the provisions of this paragraph (5), in respect of any
         loss, claim, damage or liability based upon any untrue or alleged
         untrue statement of a material fact or omission or alleged omission to
         state a material fact that relates to information other than
         information supplied by Security Holder, Security Holder shall not be
         required to contribute any amount in excess of the amount by which the
         total price at which the Registrable Securities offered by it and
         distributed to the public were offered to the public exceeds the amount
         of any damages that Security Holder has otherwise been required to pay
         by reason of such untrue or alleged untrue statement or omission or
         alleged omission. No Person guilty of fraudulent misrepresentation
         (within the meaning of Section 11(f) of the Act) shall be entitled to
         contribution from any Person who was not guilty of such fraudulent
         misrepresentation. Promptly after receipt by an indemnified party under
         this paragraph (5) of notice of the commencement of any action against
         such party in respect of which a claim for contribution may be made
         against an indemnifying party under this paragraph (5), such
         indemnified party shall notify the indemnifying party in writing of the
         commencement thereof if the notice specified in paragraph (3) above has
         not been given with respect to such

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         action; but the omission so to notify the indemnifying party shall not
         relieve it from any liability that it may have to any indemnified party
         under this paragraph (5) to the extent such omission is not
         prejudicial.

                  E. Public Availability of Information. The Company shall
comply with all public information reporting requirements of the Commission, to
the extent required from time to time to enable Security Holder to sell
Registrable Securities without registration under the Securities Act within the
limitation of the exemptions provided by (i) Rule 144 under the Securities Act,
as such Rule may be amended from time to time, or (ii) any similar rule or
regulation hereafter adopted by the Commission. Upon the request of Security
Holder, the Company will deliver to Security Holder a written statement as to
whether it has complied with such requirements.

                  F. Supplying Information. The Company shall cooperate with
Security Holder in supplying such information as may be necessary for Security
Holder to complete and file any information reporting forms presently or
hereafter required by the Commission as a condition to the availability of an
exemption from the Securities Act for the sale of any Registrable Securities.

                  G. Specific Performance. Each party hereto acknowledges and
agrees that each other party hereto would be irreparably harmed and would have
no adequate remedy of law if any of the provisions of this Agreement were not
performed in accordance with their specific terms or were otherwise breached.
Accordingly, it is agreed that, in addition to any other remedies by law or in
equity that may be available, the parties hereto shall be entitled to obtain
temporary and permanent injunctive relief with respect to any breach or
threatened breach of, or otherwise obtain specific performance of the covenants
and other agreements contained in this Agreement.

         Section 3. Representations and Warranties of the Company. The Company
represents and warrants to Security Holder that (a) the Company is a corporation
duly organized, validly existing and in good standing under the laws of the
State of Texas and has the corporate power and authority to enter into this
Agreement and to carry out its obligations hereunder, (b) the execution and
delivery of this Agreement by the Company and the consummation by the Company of
the transactions contemplated hereby have been duly authorized by all necessary
corporate action on the part of the Company and no other corporate proceedings
on the part of the Company are necessary to authorize this Agreement or any of
the transactions contemplated hereby, and (c) this Agreement has been duly
executed and delivered by the Company and constitutes a valid and binding
obligation of the Company, and, assuming this Agreement constitutes a valid and
binding obligation of Security Holder, is enforceable against the Company in
accordance with its terms, subject to applicable bankruptcy, reorganization,
insolvency, moratorium, fraudulent conveyance and similar laws affecting
creditors' rights generally from time to time and to general principles of
equity, and except as the enforceability thereof may be limited by
considerations of public policy.

         Section 4. Representations and Warranties of Security Holder. Security
Holder represents and warrants to the Company that (a) Security Holder is a
corporation duly organized, validly existing and in good standing under the laws
of the State of Delaware and has the corporate power and authority to enter into
this Agreement and to carry out its obligations hereunder, (b) the execution and
delivery of this Agreement by Security Holder and the consummation by Security
Holder of the transactions contemplated hereby have been duly authorized by all
necessary corporate action on the part of Security Holder and no other corporate
proceedings on the part of Security

                                      -10-
<PAGE>   11

Holder are necessary to authorize this Agreement or any of the transactions
contemplated hereby, and (c) this Agreement has been duly executed and delivered
by Security Holder and constitutes a valid and binding obligation of Security
Holder, and, assuming this Agreement constitutes a valid and binding obligation
of the Company, is enforceable against Security Holder in accordance with its
terms subject to applicable bankruptcy, reorganization, insolvency, moratorium,
fraudulent conveyance and similar laws affecting creditors' rights generally
from time to time and to general principles of equity, and except as the
enforceability thereof may be limited by considerations of public policy.

         Section 5. Assignment. As provided in the next sentence, this Agreement
may be assigned by Security Holder, in whole but not in part, in connection with
any transfer of all, but not a portion, of the Registrable Securities to a
Permitted Transferee except for transfers (i) in a Public Offering or (ii)
pursuant to Rule 144 or Rule 145 under the Securities Act. In order for such
transferee to be entitled to the benefits of this Agreement and thereby become
"Security Holder," such transferee must agree to be bound by this Agreement by
executing a counterpart of this Agreement. In the event of an assignment of this
Agreement pursuant to this Section 5, notices and requests to and from the
Company pursuant to this Agreement shall continue to be made only to and from
Security Holder until such time as Security Holder shall otherwise advise the
Company in writing from time to time that a transferee-Security Holder will give
and receive notices and requests.

                  In the event that any such transferee-Security Holder is an
E&P Company, then any underwriter for such E&P Company shall have customary
access to perform its due diligence obligations with respect to any Registration
Statement subject to confidentiality obligations that prohibit the sharing or
disclosure of information with such E&P Company, and no such E&P Company shall,
by virtue of this Agreement, have access to non-public information of the
Company.

                  No transfer or assignment of this Agreement shall increase the
number of Registrations that the Company is obligated to make under this
Agreement.

         Section 6. Notices. All notices and other communications hereunder
shall be in writing and shall be deemed given if delivered personally or
transmitted by telex, telegram or facsimile transmission or mailed by registered
or certified mail (return receipt requested) to the parties at the following
addresses (or at such other address for a party as shall be specified by like
notice):

                  (a)      if to Security Holder, to:

                           Shell Louisiana Onshore Properties Inc.
                           P.O. Box 7986
                           Newark, Delaware 19714
                           Attention:  Corporate Secretary

                                      -11-
<PAGE>   12

                           with a copy to:

                           Shell Oil Company
                           P.O. Box 2463
                           Houston, Texas 77252
                           Attention:  Duane C. King
                           Fax: 713-241-5362

                  (b)      if to the Company, to:

                           The Meridian Resource Corporation
                           1401 Enclave Parkway, Suite 300
                           Houston, Texas  77077
                           Attention:  Joseph A. Reeves, Jr., Chairman and
                                       Chief Executive Officer
                           Fax: (281) 558-5595

                           with a copy to:

                           Fouts & Moore, L.L.P.
                           1300 Post Oak Boulevard, 20th Floor
                           Houston, Texas  77056
                           Attention: Gary A. Messersmith
                           Fax:  (713) 986-7299

                           and a copy to:

                           Fulbright & Jaworski L.L.P.
                           1301 McKinney Street, Suite 5100
                           Houston, Texas  77010
                           Attention:  Charles L. Strauss
                           Fax:  (713) 651-5246

         Section 7. Governing Law. This Agreement shall be governed by and
construed in accordance with the laws of the State of Texas.

         Section 8. Counterparts. This Agreement may be executed in any number
of counterparts, which together shall constitute a single agreement.

                                      -12-
<PAGE>   13

         IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
duly executed by their officers thereunto duly authorized.

                                         THE MERIDIAN RESOURCE CORPORATION

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

                                         SHELL LOUISIANA ONSHORE PROPERTIES INC.

                                         By:          /s/ R.V. Deere
                                            ------------------------------------
                                         Name:            R.V. Deere
                                              ----------------------------------
                                         Title:           Treasurer
                                               ---------------------------------

                                      -13-<PAGE>   1
                                                                     EXHIBIT 4.3
================================================================================

                        THE MERIDIAN RESOURCE CORPORATION

                                       AND

                       AMERICAN STOCK TRANSFER & TRUST CO.

                                  RIGHTS AGENT

                               AMENDMENT NO. 1 TO

                                RIGHTS AGREEMENT

                          DATED AS OF JANUARY 29, 2001

================================================================================
<PAGE>   2

                                 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."
<PAGE>   3

         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."

                                      -2-
<PAGE>   4

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

                                      -3-

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