CERTIFICATE OF DESIGNATIONS, RIGHTS AND PREFERENCES
of
SERIES A CUMULATIVE CONVERTIBLE PREFERRED STOCK
of
TRANSMERIDIAN EXPLORATION INCORPORATED

        TRANSMERIDIAN EXPLORATION INCORPORATED, a Delaware corporation (the "Corporation"), pursuant to Section 151 of the General Corporation Law of the State of Delaware, does hereby make this Certificate of Designations, Rights and Preferences and does hereby state and certify that pursuant to the authority expressly vested in the Board of Directors of the Corporation (the "Board") by the Certificate of Incorporation of the Corporation, as amended and restated to date (the "Certificate of Incorporation"), which authorizes the issuance of 5,000,000 shares of preferred stock, $0.0006 per share, in one or more series, the Board duly adopted the following resolutions, which resolutions remain in full force and effect as of the date hereof:

        RESOLVED, that, pursuant to Article 15 of the Certificate of Incorporation the Board hereby authorizes the issuance of, and fixes the designation and preferences and relative, participating, optional and other special rights, and qualifications, limitations and restrictions, of a series of preferred stock of the Corporation consisting of 1,785.714 shares, par value $0.0006 per share, to be designated "Series A Cumulative Convertible Preferred Stock" (hereinafter, the "Preferred Stock"); and be it

        RESOLVED, that each share of Preferred Stock shall rank equally in all respects, shall be convertible into shares of the common stock of the Corporation, par value $0.0006 per share (the "Common Stock") as provided herein and shall be subject to the following terms and provisions:

        1.     Dividends. The holders of the Preferred Stock shall be entitled to receive, when, if and as declared by the Corporation's Board of Directors, out of funds legally available therefor, cumulative dividends payable as set forth in this Section 1.

        (a)   Dividends on the Preferred Stock shall accrue from the date of original issuance of the shares of Preferred Stock (the "Date of Original Issue"), shall be cumulative from the Date of Original Issue, and such dividends shall be payable, whether or not earned or declared by the Board of Directors of the Corporation. Until paid, the right to receive dividends on the Preferred Stock shall accumulate, and shall be payable in cash as set forth below, in arrears, on March 31, June 30, September 30 and December 31 of each year (each, a "Dividend Payment Date"), commencing on December 31, 2004 (the "Initial Dividend Payment Date") except that if such Dividend Payment Date is not a business day, then the Dividend Payment Date will be the immediately preceding business day. Each such dividend declared by the Board of Directors on the Preferred Stock shall be paid to the holders of record of shares of the Preferred Stock as they appear on the stock register of the Corporation on the record date which shall be the business day next preceding a Dividend Payment Date. Dividends in arrears for any past dividend period may be declared by the Board of Directors of the Corporation and paid on shares of the Preferred Stock on any date fixed by the Board of Directors of the Corporation, whether or not a regular Dividend Payment Date, to holders of record of shares of the Preferred Stock as they appear on the Corporation's stock register on the record date. Any dividend payment made on shares of the Preferred Stock shall first be credited against the dividends accumulated with respect to the earliest dividend period for which dividends have not been paid.

        (b)   The dividend rate (the "Dividend Rate") on each share of Preferred Stock shall be 4.5% per share per annum on $14,000 (the Liquidation Preference (as defined below) of each such share) for the period from the Date of Original Issue until the Initial Dividend Payment Date and, for each dividend period thereafter, which shall commence on the last day of the preceding dividend period and shall end on the next Dividend Payment Date, shall be at the Dividend Rate (as adjusted from time to time as hereinafter provided) on such Liquidation Preference. For the period ending on the Initial Dividend Payment Date, the amount of dividends per share of the Preferred Stock shall be computed by

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