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                                                                     EXHIBIT 3.4

                         CERTIFICATE OF AMENDMENT OF THE
                          CERTIFICATE OF INCORPORATION

         Texas Capital Bancshares, Inc., a corporation organized and existing
under and by virtue of Section 242 of the General Corporation Law of the State
of Delaware (the "Corporation"),

         DOES HEREBY CERTIFY:

         FIRST: That the Board of Directors of said Corporation, adopted a
resolution proposing and declaring the following amendments to the Certificate
of Incorporation of said Corporation:

         RESOLVED, that ARTICLE IV of the Certificate of Incorporation is hereby
amended in its entirety to read as follows:

                                   "ARTICLE IV

                  The total number of shares of capital stock which the
         Corporation shall have the authority to issue is twenty million
         (20,000,000) shares of Common Stock, $.01 par value and two million
         five hundred thousand (2,500,000) shares of Preferred Stock, $.01 par
         value. Unless specifically provided otherwise herein, the holders of
         Common Stock shall be entitled to one vote for each share held in any
         stockholder vote in which any of such holders is entitled to
         participate. The board of directors may determine the powers,
         designations, dividend rate, if any, preferences and relative,
         participating, optional or other special rights, including voting
         rights, and the qualifications, limitations or restrictions thereof, of
         each class of capital stock and of each series within any such class
         and may increase or decrease the number of shares within each such
         class or series; provided, however, that the board of directors may not
         decrease the number of shares within a class or series to less than the
         number of shares within such class or series that are then issued and
         may not increase the number of shares within a series above the total
         number of authorized shares of the applicable class for which the
         powers, designations, preferences and rights have not otherwise been
         set forth herein. Attached hereto as Exhibit "A" and incorporated
         herein by reference is a statement of the rights, preferences,
         privileges, restrictions and other terms in respect of the first series
         of Common Stock, designated as Series A-1 Nonvoting Common Stock."

         SECOND: That in lieu of a meeting and vote of stockholders, the
stockholders have given written consent to said amendment in accordance with the
provisions of Section 228 of the General Corporation Law of the State of
Delaware.

         IN WITNESS WHEREOF, said Corporation has caused this certificate to be
signed by Joseph M. Grant, its Secretary, this 9th day of December, 1998.


                                                     /s/ JOSEPH M. GRANT
                                                     ---------------------------
                                                     Joseph M. Grant, Secretary





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                                   EXHIBIT "A"

                         TEXAS CAPITAL BANCSHARES, INC.

                      CERTIFICATE OF POWERS, DESIGNATIONS,
                            PREFERENCES AND RIGHTS OF
                        SERIES A-1 NONVOTING COMMON STOCK

         The powers, designations, preferences and rights of the Series A-1
Nonvoting Common Stock ("Series A-1 Common Stock") of Texas Capital Bancshares,
Inc. (the "Corporation") are as follows:

                  (a) Voting Rights. The holders of Series A-1 Common Stock
         shall not have any voting rights, except as otherwise required by
         applicable law, in which case holders of Series A-1 Common Stock shall
         vote (at the rate of one vote per share of Series A-1 Common Stock
         held) as a single class on such matter unless otherwise required by
         law.

                  (b) Dividends. The Board of Directors of the Corporation may
         cause dividends to be paid to the holders of shares of Common Stock and
         Series A-1 Common Stock out of funds legally available for the payment
         of dividends by declaring an amount per share as a dividend. When and
         as dividends or other distributions (including without limitations any
         grant or distribution of rights to subscribe for or purchase shares of
         capital stock or securities or indebtedness convertible into capital
         stock of the Corporation) are declared, whether payable in cash, in
         property or in shares of stock of the Corporation (subject to the
         limitations set forth herein), the holders of Common Stock and Series
         A-1 Common Stock shall be entitled to share equally, share for share,
         in such dividends or other distributions as if all such shares were of
         a single class. No dividends or other distributions shall be declared
         or paid in shares of Common Stock or Series A-1 Common Stock or
         options, warrants or rights to acquire such stock or securities
         convertible into or exchangeable for shares of such stock, except
         dividends or other distributions payable to all of the holders of
         Common Stock and Series A-1 Common Stock ratably according to the
         number of shares of Common Stock and Series A-1 Common Stock held by
         them, in shares of Common Stock to holders of that class of stock and
         Series A-1 Common Stock to holders of that class of stock.

                  (c) Liquidation Rights. In the event of any voluntary or
         involuntary liquidation, dissolution or winding up of the affairs of
         the Corporation holders of Common Stock and Series A-1 Common Stock
         shall be entitled to share equally, share for share, in all assets of
         the Corporation available for distribution to its stockholders as if
         all such shares were of a single class.

                  (d) Conversion.

                           (1) Each share of Series A-1 Common Stock shall be
                  convertible into one share of Common Stock, solely to increase
                  a holder's ownership to no more than 4.9% of the Corporation's
                  fully diluted Common Stock, upon delivery to the Corporation
                  of a certificate (and a legal opinion if requested by the
                  Corporation), signed by or on behalf of the holder or holders
                  seeking such conversion, to the effect that after such
                  conversion such holder or holders will not own more than 4.9%
                  of the Common Stock. Any conversion of shares of Series A-1
                  Common Stock into shares of Common Stock pursuant to this
                  Clause (d)(1) shall be effected by the delivery to the
                  Corporation at its principal executive office of the
                  certificates representing shares to be converted, duly
                  endorsed, together with written instructions that the shares
                  are to be converted, and accompanied by the required
                  certificate described herein.


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                           (2) The Corporation shall at all times reserve and
                  keep available out of its authorized but unissued Common
                  Stock, solely for the purpose of effecting conversions
                  pursuant to this Article, the full number of shares of Common
                  Stock issuable upon the conversion of all shares of Series A-1
                  Common Stock then outstanding and entitled to convert, and
                  shall take all such action and obtain all such permits or
                  orders as may be necessary to enable the Corporation lawfully
                  to issue such shares upon any such conversion.