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                                                                     EXHIBIT 3.1

                          CERTIFICATE OF DESIGNATION

                                      of

                    TRANSCONTINENTAL REALTY INVESTORS, INC.

                               setting forth the

            VOTING POWERS, DESIGNATIONS, PREFERENCES, LIMITATIONS,
                       RESTRICTIONS AND RELATIVE RIGHTS

                                      of

                SERIES B CUMULATIVE CONVERTIBLE PREFERRED STOCK


                        (Pursuant to Section 78.1955 of
                         the Nevada Revised Statutes)

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

     Pursuant to Section 78.1955 of the Nevada Revised Statutes ("NRS"), the
undersigned, being the President and Secretary, respectively, of
Transcontinental Realty Investors, Inc. (the "Corporation"), a Nevada
corporation, hereby certify that (a) the following resolution was duly adopted
on October 2, 2000, by the Board of Directors of the Corporation (the "Board"),
for the purposes of establishing a separate series of the Corporation's
authorized preferred stock, $0.01 par value ("Preferred Stock"), and fixing the
relative rights and preferences of such series of Preferred Stock, and (b) such
resolution has not been subsequently modified or rescinded:

     RESOLVED, that in accordance with the provisions of ARTICLE FOURTH of the
Articles of Incorporation of the Corporation, a series of Preferred Stock be,
and hereby is, created, and the voting powers, designations, preferences,
limitations, restrictions and relative, participating, optional or other special
rights of the shares of such series, and the qualifications, limitations or
restrictions thereof, be, and hereby are, as follows:

Section 1. Designation and Amount. The shares of such series shall be designated
           ----------------------
as "Series B Cumulative Convertible Preferred Stock" (the "Series B Stock") and
each share of the Series B Stock shall have a par value of $0.01 per share and a
preference on liquidation as specified in Section 6 below. The number of
authorized shares constituting the Series B Stock shall be 300,000. Such number
of shares may be increased or decreased by the Board by filing an amendment to
this Certificate of Designation, provided, however, that no decrease shall
reduce the number of shares of Series B Stock to a number less than the number
of shares then outstanding

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plus the number of shares reserved for issuance upon the exercise of outstanding
options, rights or warrants.

Section 2.  Dividends and Distributions.
            ---------------------------

     (A)  The holders of shares of Series B Stock shall be entitled to receive,
when, as, and if declared by the Board and to the extent permitted under the
NRS, out of funds legally available for the purpose and in preference to and
with priority over dividends upon all Junior Securities (as defined in Section 6
below), quarterly cumulative dividends payable in arrears in cash on the tenth
day following the end of each calendar quarter, unless such day is a Saturday,
Sunday or holiday, in which case such dividends shall be payable on the next
succeeding business day (each such date being referred to herein as a "Quarterly
Dividend Payment Date"), commencing on the first Quarterly Dividend Payment Date
after the first issuance of a share or fraction of a share of Series B Stock, in
an amount per share (rounded to the next highest cent) equal to 7.5% per annum
of the Liquidation Value (as defined in Section 6 below), as determined
immediately prior to the beginning of such calendar quarter assuming each year
consists of 360 days and each quarter consists of 90 days.

     (B)  Dividends shall commence accruing cumulatively on outstanding shares
of the Series B Stock from the date of issuance of such shares to and including
the date on which the Redemption Price (as defined in Section 9(A) below) of
such shares is paid, whether or not such dividends have been declared and
whether or not there are profits, surplus or other funds of the Corporation
legally available for the payment of such dividends. For purposes of this
Section 2, the date on which the Corporation has issued any share of Series B
Stock is its date of issuance, regardless of the number of times a transfer of
such share is made on the stock records maintained by or for the Corporation and
regardless of the number of certificates that may be issued to evidence such
share (whether by reason of transfer of such share or for any other reason).
Dividends paid on the shares of Series B Stock in an amount less than the total
amount of dividends at the time accrued and payable on such shares shall be
allocated among the holders of such shares in proportion to their respective
Unpaid Accrual Amounts, where for this purpose the "Unpaid Accrual Amount" of a
holder of shares of Series B Stock at any time equals the total of accrued
unpaid dividends on all such shares held by such holder. The Board may fix a
record date for the determination of holders of shares of Series B Stock
entitled to receive payment of a dividend or distribution declared thereon other
than a quarterly dividend paid on the Quarterly Dividend Payment Date
immediately after such dividend accrued; which record date shall be not more
than 50 days prior to the date fixed for the payment thereof.

     (C)  So long as any shares of the Series B Stock are outstanding, the
Corporation will not make, directly or indirectly, any distribution (as such
term is defined in the NRS) with respect to Junior Securities unless, on the
date specified for measuring such
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distribution, (a) all accrued dividends on the Series B Stock for all past
quarterly dividend periods have been paid in full and the full amount of accrued
dividends for the then current quarterly dividend period has been paid or
declared and a sum sufficient for the payment thereof set apart and (b) after
giving effect to such distribution (i) the Corporation would not be rendered
unable to pay its debts as they become due in the usual course of business and
(ii) the Corporation's total assets would not be less than the sum of its total
liabilities plus the amount that would be needed, if the Corporation were to be
dissolved at the time of the distribution, to satisfy the preferential rights
upon dissolution of the holders of the Series B Stock as provided in this
Certificate of Designation. Dividends shall not be paid (in full or in part) or
declared and set apart for payment (in full or in part) on any series of
Preferred Stock (including the Series B Stock) for any dividend period unless
all dividends, in the case dividends are being paid in full on the Series B
Stock, or a ratable portion of all dividends (i.e., so that the amount paid on
each share of each series of Preferred Stock as a percentage of total accrued
and unpaid dividends for all periods with respect to each such share is equal),
in the case dividends are not being paid in full on the Series B Stock, have
been or are, contemporaneously, paid and declared and set apart for payment on
all outstanding series of Preferred Stock (including the Series B Stock)
entitled thereto for each dividend period terminating on the same or earlier
date. If at any time the Corporation pays less than the total amount of
dividends then accrued with respect to the Series B Stock, such payment will be
distributed ratably among the then holders of Series B Stock so that an equal
amount is paid with respect to each outstanding share.

Section 3.  Conversion Rights.
            -----------------

     (A)  The Series B Stock may be converted at any time and from time to time
in whole or in part after October 25, 2001, at the option of the holders
thereof, in accordance with subsection (D) below at the Conversion Price (as
defined in subsection (B) below) into fully paid and nonassessable shares of
common stock, $.01 par value, of the Corporation ("Common Stock"). The number of
shares of Common Stock to be issued pursuant to such conversion shall be equal
to the number of shares offered for conversion multiplied by the Liquidation
Value per share and divided by the Conversion Price; provided, however, that (1)
as to any shares of Series B Stock which shall have been called for redemption
pursuant to Section 9, the right of conversion shall terminate upon receipt by
the holder of the notice of redemption from the Corporation and (2) on the
earlier of (a) the commencement of any liquidation, dissolution or winding up of
the Corporation by the filing of the relevant document with the Secretary of
State of the State of Nevada or with a federal bankruptcy court or (b) the
adoption by the stockholders of the Corporation of any resolution authorizing
the commencement thereof, the right of conversion shall terminate.
Notwithstanding anything to the contrary herein provided, the Corporation may
elect to redeem the shares of Series B Stock sought
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to be converted, pursuant to Section 9 hereunder, instead of issuing shares of
Common Stock in replacement thereof, in accordance with the provisions of
Section 3(D) below.

     (B)  For purposes of this Section 3, the term "Conversion Price" shall be
and mean the amount obtained (rounded upward to the next highest cent) by
multiplying (i) 0.9 by (ii) the simple average of the daily closing price of the
Common Stock for the five (5) Business Days immediately prior to the date of
conversion on the New York Stock Exchange or, if the Common Stock is not then
being traded on the New York Stock Exchange, then on the principal stock
exchange (including without limitation The Nasdaq Stock Market) on which the
Common Stock is then listed or admitted to trading as determined by the
Corporation ("Principal Stock Exchange") or, if the Common Stock is not then
listed or admitted to trading on a Principal Stock Exchange, the average of the
last reported closing bid and asked prices on such days in the over-the-counter
market or, if no such prices are available, the fair market value per share of
the Common Stock, as determined by the Board in its sole discretion. The
Conversion Price shall not be subject to any adjustment as a result of the
issuance of any additional shares of Common Stock by the Corporation for any
purpose, except for stock splits (whether accomplished by stock dividends or
otherwise) or reverse stock splits occurring during the five (5) Business Days
referenced in the calculation of the Conversion Price. For purposes of
calculating the Conversion Price, the term "Business Day" shall mean a day on
which the Principal Stock Exchange is open for business or, if no such exchange,
the term "Business Day" shall have the meaning given such term in Section 3(D)
below.

     (C)  Upon any conversion, fractional shares of Common Stock shall not be
issued but any fractions shall be adjusted by the delivery of one additional
share of Common Stock in lieu of any cash. Any accrued but unpaid dividends
shall be convertible into shares of Common Stock as provided for in this
Section. The Corporation shall pay all issue taxes, if any, incurred in respect
to the issuance of Common Stock on conversions, provided, however, that the
Corporation shall not be required to pay any transfer or other taxes incurred by
reason of the issuance of such Common Stock in names other than those in which
the Series A Stock surrendered for conversion may stand.

     (D)  Any conversion of Series B Stock into Common Stock shall be made by
the surrender to the Corporation, at the office of the Corporation set forth in
Section 11 hereof or at the office of the transfer agent for such shares, of the
certificate or certificates representing the Series B Stock to be converted,
duly endorsed or assigned (unless such endorsement or assignment be waived by
the Corporation) together with a written request for conversion. The Corporation
shall either (i) issue as of the date of receipt by the Corporation of such
surrender shares of Common Stock calculated as provided above and evidenced by a
stock certificate delivered to the holder as soon as practicable after the date
of such surrender; or (ii) within two (2) Business Days (unless otherwise
provided,
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"Business Day" herein shall mean any day other than a Saturday, a Sunday or a
day on which banking institutions in Dallas, Texas are authorized or obligated
by law or executive order to remain closed) after the date of such surrender
advise the holder of the Series B Stock that the Corporation is exercising its
option to redeem the Series B Stock pursuant to Section 9, in which case the
Corporation shall have sixty (60) days from the date of such surrender to pay to
the holder cash in an amount equal to the Redemption Price (as defined in
Section 9(A) below) for each share of Series B Stock so redeemed. The date of
surrender of any Series B Stock shall be the date of receipt by the Corporation
or its agent of such surrendered shares of Series B Stock.

     (E)  A number of authorized shares of Common Stock sufficient to provide
for the conversion of the Series B Stock outstanding upon the basis hereinbefore
provided shall at all times be reserved for such conversion. If the Corporation
shall propose to issue any securities or to make any change in its capital
structure which would change the number of shares of Common Stock into which
each share of Series B Stock shall be convertible as herein provided, the
Corporation shall at the same time also make proper provision so that thereafter
there shall be a sufficient number of share of Common Stock authorized and
reserved for conversion of the outstanding Series B Stock on the new basis.

     (F)  In case the Corporation shall propose at any time before all shares of
the Series B Stock have been redeemed by the Corporation or converted into
Common Stock:

         (i)   to pay any dividend on the Common Stock outstanding payable in
     Common Stock or to make any other distribution, other than cash dividends
     to the holders of the Common Stock outstanding; or

         (ii)  to offer for subscription to the holders of the Common Stock
     outstanding any additional shares of any class or any other rights or
     option; or

         (iii) to effect any re-classification or recapitalization of the Common
     Stock outstanding involving a change in the Common Stock, other than a
     subdivision or combination of the Common Stock outstanding; or

         (iv) to merge or consolidate with or into any other corporation (unless
     the Corporation is the surviving entity and holders of Common Stock
     continue to hold such Common Stock without modification and without receipt
     of any additional consideration), or to sell, lease, or convey all or
     substantially all its property or business, or to liquidate, dissolve or
     wind up;

then, in each such case, the Corporation shall mail to the holders of record of
each of the shares of Series B Stock at their last known address as shown by the
Corporation's records a statement, signed by an officer of the Corporation, with
respect to the
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proposed action. Such statement shall be so mailed at least thirty (30) days
prior to the date of the taking of such action or the record date for holders of
the Common Stock for the purposes thereof, whichever is earlier. If such
statement relates to any proposed action referred to in clauses (iii) or (iv) of
this subsection (F), it shall set forth such facts with respect thereto as shall
reasonably be necessary to inform the holders of the Series B Stock as to the
effect of such action upon the conversion rights of such holders.

Section 4.  Voting Rights and Powers. The holders of shares of Series B Stock
            ------------------------
shall have only the following voting rights:

     (A)  Each holder of outstanding shares of the Series B Stock shall be
   entitled to vote the number of votes equal to the number of shares of the
   Series B Stock held by such person at each meeting of the stockholders of the
   Corporation (or actions by written consent of the stockholders of the
   Corporation in lieu of meetings) with respect to any and all matters
   presented to the stockholders of the Corporation for their action or
   consideration.

     (B)  The outstanding shares of the Series B Stock shall not be counted in
   determining the total number of outstanding shares to constitute a quorum at
   any meeting of the stockholders of the Corporation.

     (C)  The Corporation shall not amend, alter or repeal preferences, rights,
   powers or other terms of the Series B Stock so as to affect adversely the
   Series B Stock, without the written consent or affirmative vote of the
   holders of a majority of the then outstanding shares of Series B Stock,
   either at a meeting of the holders of the Series B Stock or by written
   consent in lieu of a meeting.

Section 5. Reacquired Shares. Any shares of Series B Stock purchased or
           -----------------
otherwise acquired by the Corporation in any manner whatsoever or surrendered
for conversion shall no longer be deemed to be outstanding and all rights with
respect to such shares of stock, including the right, if any, to receive notices
and to vote, shall forthwith cease, except, in the case of stock surrendered for
conversion hereunder, rights of the holder thereof to receive Common Stock in
exchange therefor. All shares of Series B Stock obtained by the Corporation
shall be retired and canceled promptly after the acquisition thereof. All such
shares shall upon their cancellation become authorized but unissued shares of
Preferred Stock and may be reissued as part of a new series of Preferred Stock
subject to the conditions and restrictions on issuance set forth herein, in the
Articles of Incorporation, or in any other Certificates of Designations creating
a series of Preferred Stock or any similar stock or as otherwise required by
law.

Section 6. Liquidation, Dissolution or Winding Up. The Liquidation Value of the
           --------------------------------------
Series B Stock shall be $5.00 per share.
<PAGE>

Upon any liquidation, dissolution or winding up of the Corporation, and after
paying and providing for the payment of all creditors of the Corporation, the
holders of shares of the Series B Stock then outstanding shall be entitled,
before any distribution or payment is made upon the Common Stock and any other
equity security of any kind, other than Preferred Stock, which the Corporation
at any time has issued, issues or is authorized to issue (collectively, "Junior
Securities"), to receive a liquidation preference in an amount in cash equal to
the Adjusted Liquidation Value as of the date of such payment, whether such
liquidation is voluntary or involuntary, and the holders of the Series B Stock
shall not be entitled to any other or further distributions of the assets. If,
upon any liquidation, dissolution or winding up of the affairs of the
Corporation, the net assets available for distribution shall be insufficient to
permit payment to the holders of all outstanding shares of all series of
Preferred Stock of the amount to which they respectively shall be entitled, then
the assets of the Corporation to be distributed to such holders will be
distributed ratably among them based upon the amounts payable on the shares of
each such series of Preferred Stock in the event of voluntary or involuntary
liquidation, dissolution or winding up, as the case may be, in proportion to the
full preferential amounts, together with any and all arrearages to which they
are respectively entitled. Upon any such liquidation, dissolution or winding up
of the Corporation, after the holders of Preferred Stock have been paid in full
the amounts to which they are entitled, the remaining assets of the Corporation
may be distributed to holders of Junior Securities, including Common Stock, of
the Corporation. The Corporation will mail written notice of such liquidation,
dissolution or winding up, not less than twenty (20) nor more than fifty (50)
days prior to the payment date stated therein to each record holder of Series B
Stock. Neither the consolidation nor merger of the Corporation into or with any
other corporation or corporations, nor the sale or transfer by the Corporation
of less than all or substantially all of its assets, nor a reduction in the
capital stock of the Corporation, nor the purchase or redemption by the
Corporation of any shares of its Preferred Stock or Common Stock or any other
class of its stock will be deemed to be a liquidation, dissolution or winding up
of the Corporation within the meaning of this Section 6. "Adjusted Liquidation
Value" shall mean the Liquidation Value as defined in this Section 6 plus all
accrued and unpaid dividends through the applicable date.

Section 7. Ranking. Except as provided in the following sentence, the Series B
           -------
Stock shall rank on a parity as to dividends and upon liquidation, dissolution
or winding up with all other shares of Preferred Stock issued by the
Corporation. The Corporation shall not issue any shares of Preferred Stock of
any series which are superior to the Series B Stock as to dividends or rights
upon liquidation, dissolution or winding up of the Corporation as long as any
shares of the Series B Stock are issued and outstanding, without the prior
written consent of the holders of at least a majority of such shares of Series B
Stock then outstanding voting separately as a class.
<PAGE>

Section 8.  Redemption at the Option of the Holder.
            ---------------------------------------

     (A)  The shares of Series B Stock shall be redeemable for cash at the
  option of the holder of Series B Stock at any time after October 25, 2001 by
  giving written notice to the Corporation, at the office of the Corporation set
  forth in Section 11 hereof. The cash to be paid to the holder pursuant to such
  redemption shall be the Redemption Price (as defined in Section 9); provided,
  however, that the right of redemption shall terminate on the earlier of (i)
  the commencement of any liquidation, dissolution or winding up of the
  Corporation by the filing of the relevant documents with the Secretary of
  State of Nevada or with a federal bankruptcy court or (ii) the adoption by the
  stockholders of the Corporation of any resolution authorizing the commencement
  thereof.

     (B)  Upon receipt of the written request for redemption, the Corporation
  shall provide the holder of the certificate or certificates of Series B Stock
  to be redeemed with: (i) the date on which the payment of cash will be
  available, which date shall be no later than thirty (30) days after the
  receipt of the written request; and (ii) the place at or the manner in which
  the holder of the Series B Stock to be redeemed may surrender the certificate
  or certificates representing the Series B Stock to be redeemed and obtain
  payment of the applicable Redemption Price.

Section 9.  Redemption at the Option of the Corporation
            --------------------------------------------

     (A)  The Corporation shall have the right to redeem all or a portion of the
   Series B Stock issued and outstanding at any time and from time to time, at
   its option, for cash. The redemption price of the Series B Stock pursuant to
   this Section 9 shall be an amount per share equal to the Adjusted Liquidation
   Value as of the Redemption Date (the "Redemption Price").

      (B) The Corporation may redeem all or a portion of any holder's shares of
   Series B Stock by giving such holder not less than twenty (20) days nor more
   than thirty (30) days notice thereof prior to the date on which the
   Corporation desires such shares to be redeemed, which date shall be a
   Business Day (the "Redemption Date"). Such notice shall be in writing and
   shall be hand delivered or mailed, postage prepaid, to the holder (the
   "Redemption Notice"). If mailed, such notice shall be deemed to be delivered
   when deposited in the United States Mail, postage prepaid, addressed to the
   holder of shares of Series B Stock at his address as it appears on the stock
   transfer records of the Corporation. The Redemption Notice shall state (i)
   the total number of shares of Series B Stock held by such holder; (ii) the
   total number of shares of the holder's Series B Stock that the Corporation
   intends to redeem; (iii) the Redemption Date and the Redemption Price; and
   (iv) the place at which the holder(s) may obtain payment of the applicable
   Redemption Price upon surrender of the share certificate(s).
<PAGE>

     (C)  If fewer than all shares of the Series B Stock at any time outstanding
   shall be called for redemption, such shares shall be redeemed pro rata, by
   lot drawn or other manner deemed fair in the sole discretion of the Board of
   Directors to redeem one or more such shares without redeeming all such shares
   of Series B Stock. If a Redemption Notice shall have been so mailed, at least
   two (2) Business Days prior to the Redemption Date the Corporation shall
   provide for payment of a sum sufficient to redeem the applicable number of
   shares of Series B Stock subject to redemption either by (i) setting aside
   the sum required to be paid as the Redemption Price by the Corporation,
   separate and apart from its other funds, in trust for the account of the
   holder(s) of the shares of Series B Stock to be redeemed or (ii) depositing
   such sum in a bank or trust company (either located in the state where the
   principal executive office of the Corporation is maintained, such bank or
   trust company having a combined surplus of at least $20,000,000 according to
   its latest statement of condition, or such other bank or trust company as may
   be permitted by the Articles of Incorporation, or by law) as a trust fund,
   with irrevocable instructions and authority to the bank or trust company to
   give or complete the notice of redemption and to pay, on or after the
   Redemption Date, the applicable Redemption Price on surrender of certificates
   evidencing the share(s) of Series B Stock so called for redemption and, in
   either event, from and after the Redemption Date (a) the share(s) of Series B
   Stock shall be deemed to be redeemed, (b) such setting aside or deposit shall
   be deemed to constitute full payment for such shares(s), (c) such share(s) so
   redeemed shall no longer be deemed to be outstanding, (d) the holder(s)
   thereof shall cease to be a shareholder of the Corporation with respect to
   such share(s), and (e) such holder(s) shall have no rights with respect
   thereto except the right to receive the Redemption Price for the applicable
   shares. Any interest on the funds so deposited shall be paid to the
   Corporation. Any and all such redemption deposits shall be irrevocable except
   to the following extent: any funds so deposited which shall not be required
   for the redemption of any shares of Series B Stock because of any prior sale
   or purchase by the Corporation other than through the redemption process,
   subsequent to the date of deposit but prior to the Redemption Date, shall be
   repaid to the Corporation forthwith and any balance of the funds so deposited
   and unclaimed by the holder(s) of any shares of Series B Stock entitled
   thereto at the expiration of one calendar year from the Redemption Date shall
   be repaid to the Corporation upon its request or demand therefor, and after
   any such repayment of the holder(s) of the share(s) so called for redemption
   shall look only to the Corporation for payment of the Redemption Price
   thereof. All shares of Series B Stock redeemed shall be canceled and retired
   and no shares shall be issued in place thereof, but such shares shall be
   restored to the status of authorized but unissued shares of Preferred Stock.

          (D)  Holders whose shares of Series B Stock have been redeemed
   hereunder shall surrender the certificate or
<PAGE>

     certificates representing such shares, duly endorsed or assigned (unless
     such endorsement or assignment be waived by the Corporation), to the
     Corporation by mail, courier or personal delivery at the Corporation's
     principal executive office or other location so designated in the
     Redemption Notice, and upon the Redemption Date the Redemption Price shall
     be payable to the order of the person whose name appears on such
     certificate or certificates as the owner thereof, and each surrendered
     certificate shall be canceled and retired. In the event fewer than all of
     the shares represented by such certificates are redeemed, a new certificate
     shall be issued representing the unredeemed shares.

Section 10. Sinking Fund. The Corporation shall not be required to maintain any
            ------------
so-called "sinking fund" for the retirement on any basis of the Series B Stock.

Section 11. Notice. Any notice or request made to the Corporation in connection
            ------
with the Series B Stock shall be given, and shall conclusively be deemed to have
been given and received three (3) Business Days following deposit thereof in
writing, in the U.S. mails, certified mail, return receipt requested, duly
stamped and addressed to the Corporation, to the attention of its General
Counsel, at its principal executive offices (which shall be deemed to be the
address most recently provided to the Securities and Exchange Commission ("SEC")
as its principal executive offices for so long as the Corporation is required to
file reports with the SEC).

     IN WITNESS WHEREOF, this Certificate of Designation is executed on behalf
of the Corporation by its President and its Secretary as of the 20th day of
October, 2000.

                                             /s/ Karl L. Blaha
                                             -----------------------------------
                                             Karl L. Blaha, President

                                             /s/ Robert A. Waldman
                                             -----------------------------------
                                             Robert A. Waldman, Secretary

STATE OF TEXAS       (S)
                     (S)
COUNTY OF DALLAS     (S)

     This instrument was acknowledged before me on October 20, 2000 by Karl L.
Blaha.

                                             /s/ Carolyn A. Stefanek
                                             -----------------------------------
                                             Notary Public, State of Texas