EXHIBIT 3.4

                          CERTIFICATE OF INCORPORATION

                                       OF

                       TEXAS MERIDIAN FINANCE CORPORATION

      FIRST: The name of the Corporation is Texas Meridian Finance Corporation.

      SECOND: The registered office of the Corporation in the State of Delaware
is located at Corporation Trust Center, 1209 Orange Street in the City of
Washington, County of New Castle. The name and address of its registered agent
is The Corporation Trust Company, Corporation Trust Center, 1209 Orange Street,
Wilmington, Delaware.

      THIRD: The name of the business and purposes to be conducted or promoted
by the Corporation is to engage in any lawful act or activity for which
corporations may be organized under the General Corporation Law of Delaware.

      FOURTH: The total number of shares of stock that the Corporation shall
have authority to issue is 1,000 shares of common stock of the par value of
$1.00 each.

      FIFTH:      The name and mailing address of the incorporation is:

            Name                           Mailing Address
            ----                           ---------------
      Martin F. Doublesin            1301 McKinney, Suite 5100
                                     Houston, Texas  77010-3095

      SIXTH: The names and mailing addresses of the persons who are to serve as
directors of the Corporation until the first annual meeting of the stockholders
or until their successors are elected and qualify are:

            Name                           Mailing Address
            ----                           ---------------
      Joseph A. Reeves, Jr.          15995 N. Barkers Landing, Suite 300
                                     Houston, Texas  77079

      Michael J. Mayell              15995 N. Barkers Landing, Suite 300
                                     Houston, Texas  77079

      SEVENTH: Elections of directors need not be by written ballot unless the
by-laws of the Corporation shall so provide. The Board of Directors is expressly
authorized to adopt, amend or repeal the by-laws of the Corporation.

      EIGHTH: A director of the Corporation shall not be personally liable to
the Corporation or its stockholders for monetary damages for breach of fiduciary
duty as a director, except for liability (i) for any breach of the director's
duty of loyalty to the Corporation or its stockholders, (ii) for acts of
omissions not in good faith or which involve intentional misconduct or a knowing
violation of law, (iii) under Section 174 of the General Corporation Law of the
State of Delaware, or (iv) for any transaction from which the director derived
an improper personal benefit. If the Delaware General Corporation Law hereafter
is amended to authorize the further elimination or limitation of the liability
of directors, then the liability of a director of the Corporation, in addition
to the limitation on personal liability provided herein, shall be limited to the
fullest extent permitted by the amended Delaware General Corporation Law. Any
repeal or modification of this paragraph by the stockholders of the Corporation
shall be prospective only, and shall not adversely affect any limitation on the
personal liability of a director of the Corporation existing at the time of such
repeal or modification.

      The undersigned, being the incorporator hereinbefore named, for the
purpose of forming a corporation pursuant to the General Corporation Law of the
State of Delaware, does make this Certificate, hereby declaring and certifying
that this is my act and deed and the facts herein stated are true, and
accordingly have hereunto set my hand this 10th day of December, 1993.

                                            /s/  Martin F. Doublesin
                                            -----------------------------
                                                 Martin F. Doublesin

                                     - 2 -

                       TEXAS MERIDIAN FINANCE CORPORATION

                            CERTIFICATE OF AMENDMENT
                                       TO
                          CERTIFICATE OF INCORPORATION

      Texas Meridian Finance Corporation (the "Company"), a corporation
organized and existing under and by virtue of the General Corporation Law of the
State of Delaware ("DGCL"), does hereby certify:

      FIRST: That the Board of Directors of the Company, by Written Consent of
Directors in Lieu of Special Meeting dated June 27, 1997, unanimously adopted
resolutions proposing and declaring advisable the following amendment to the
Certificate of Incorporation of the Company and directed that such amendment be
considered by the sole stockholder of the Company:

      To amend Article First of the Certificate of Incorporation in its entirety
to read as follows:

            "First: The name of the corporation is The Meridian Resource
      Corporation."

      SECOND: That the Written Consent of the Sole Stockholder in Lieu of
Special Meeting dated June 27, 1997, in accordance with Section 228 of the DGCL,
the holder of all of the shares of Common Stock of the Company entitled to vote
on such amendment voted in favor of such amendment.

      THIRD: That the aforesaid amendments were duly adopted in accordance with
the applicable provisions of Section 242 of the DGCL.

      IN WITNESS WHEREOF, the Company has caused this Certificate to be signed
on June 27, 1997, by Joseph a. Reeves, Jr., its Chairman of the Board and Chief
Executive Officer.

                                    TEXAS MERIDIAN FINANCE CORPORATION

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