<PAGE>   1
                                                                     EXHIBIT 4.2


                          INTROGEN THERAPEUTICS, INC.,

                         CERTIFICATE OF DESIGNATIONS OF
                 SERIES A NON-VOTING CONVERTIBLE PREFERRED STOCK

                  Pursuant to Section 151 of the General Corporation Law of the
State of Delaware, David G. Nance and Rodney Varner, being the Chief Executive
Officer and Secretary, respectively, of Introgen Therapeutics, Inc., a Delaware
corporation (the "Company"),

                  DO HEREBY CERTIFY:

                  FIRST, that they are the duly elected Chief Executive Officer
and Secretary, respectively, of the Company.

                  SECOND, that pursuant to the authority conferred upon the
Company's Board of Directors (the "Board") by Article Four of the Company's
Restated Certificate of Incorporation filed with the Delaware Secretary of State
on October 17, 2000 (the "Restated Certificate"), the Board on June 30, 2001
adopted the following recitals and resolutions creating a new series of
preferred stock designated as Series A Non-Voting Convertible Preferred Stock
(the "Series A Preferred):

                  WHEREAS, the Restated Certificate provides for two authorized
         classes of stock known as Common Stock and Preferred Stock, the
         Preferred Stock being issuable from time to time in one or more series;

                  WHEREAS, the Board is authorized by the Restated Certificate
         to determine the powers, rights, preferences, limitations and
         restrictions granted to or imposed upon any wholly unissued series of
         Preferred Stock, to fix the number of shares constituting any such
         series, and to determine the designation thereof, or any of them; and

                  WHEREAS, the Board desires, pursuant to its authority as
         aforesaid, to determine and fix the powers, rights, preferences,
         limitations and restrictions relating to a series of Preferred Stock
         and the number of shares constituting, and the designation of, such
         series;

                  NOW, THEREFORE, BE IT RESOLVED, that pursuant to the authority
         vested in the Board in accordance with the provisions of the Restated
         Certificate, a new series of Preferred Stock to be designated "Series A
         Non-Voting Convertible Preferred Stock," be, and it hereby is, created,
         and the Board hereby fixes and determines the designation of, the
         number of shares constituting, and the rights, preferences, privileges
         and restrictions relating to, such series of Preferred Stock as follows
         (all terms used herein which are not otherwise defined shall have the
         meanings set forth in the Restated Certificate):



<PAGE>   2


                  Section 1. Designation of Series, Amount and Par Value. The
         series of preferred stock shall be designated as "Series A Non-Voting
         Convertible Preferred Stock", and the number of shares so designated
         shall be one hundred thousand (100,000) (which number shall not be
         subject to increase without the consent of the holders of at least a
         majority of the Series A Preferred). Each share of Series A Preferred
         shall have a par value of $0.001.

                  Section 2. Voting Rights. Except as otherwise provided herein
         and as otherwise required by law, the holders of the Series A Preferred
         shall not have any right or power to vote. On any matter on which the
         holders of the Series A Preferred shall be entitled to vote, each share
         of Series A Preferred shall entitle the holder thereof to cast a number
         of votes equal to the number of votes that could be cast by a holder of
         the Common Stock into which such share of Series A Preferred is
         convertible on the applicable record date for such vote.

                  Section 3. Dividends. The holders of the Series A Preferred
         shall be entitled to receive, on a pari passu basis with the holders of
         Common Stock, such dividends as may be declared from time to time by
         the Board, provided, however, that for this purpose each share of
         Series A Preferred shall be entitled to receive an amount of dividends
         equal to product of multiplying (a) the number of shares of Common
         Stock into which such share of Series A Preferred is convertible by (b)
         the dividend amount for each share of Common Stock.

                  Section 4. Conversion.

                  (a) Right to Convert. Each share of Series A Preferred shall
         be convertible, at the option of the holder thereof, at any time after
         the date of issuance of such share, into that number of fully paid and
         nonassessable shares of the Common Stock as is determined using the
         Conversion Ratio (as defined in Section 4(e)); provided, however, that
         no such conversion shall become effective unless and until any and all
         legal requirements associated with such conversion, including but not
         limited to any necessary filing under the Hart-Scott-Rodino Antitrust
         Improvements Act of 1976, as amended ("HSR Act"), and the expiration of
         any applicable waiting period thereunder, shall have been satisfied.

                  (b) Conversion at the Election of the Company. All shares of
         Series A Preferred shall be converted into that number of fully paid
         and nonassessable shares of Common Stock as is determined using the
         Conversion Ratio (as defined in Section 4(e)), at any time on or after
         August 1, 2001, upon a resolution of the Board to such effect;
         provided, however, that no such conversion shall become effective
         unless and until any and all legal requirements associated with such
         conversion, including but not limited to any necessary filing under the
         HSR Act and the expiration of any applicable waiting period thereunder,
         shall have been satisfied. Upon the adoption of such a resolution and
         conversion of shares of Series A Preferred into shares of Common Stock
         pursuant to this Section 4(b), the Company shall promptly deliver to
         each former holder of shares of Series A Preferred a notice


                                       2


<PAGE>   3


         ("Conversion Notice") advising such holder of (i) such conversion and
         the effective date thereof; (ii) the number of shares of Common Stock
         issuable to such holder upon conversion of the shares of Series A
         Preferred held by such holder and (iii) the address to which such
         holder should return the certificate or certificates representing the
         shares of Series A Preferred held by such holder in order to receive a
         certificate evidencing the shares of Common Stock issuable to such
         holder upon conversion. The Conversion Notice shall be accompanied by a
         true and correct copy of the resolution of the Board that effected the
         conversion of the Series A Preferred.

                  (c) Conversion Date. The date upon which shares of Series A
         Preferred convert to shares of Common Stock pursuant to Section 4(a) or
         4(b) shall be referred to as the "Conversion Date".

                  (d) Delivery of Certificates for Shares of Common Stock Issued
         Upon Conversion. Upon the conversion of shares of Series A Preferred
         into shares of Common Stock, the Company shall promptly deliver to each
         holder of Series A Preferred a certificate or certificates representing
         the number of shares of Common Stock issued upon the conversion of
         shares of Series A Preferred. Notwithstanding the foregoing, the
         Company shall not be obligated to issue a certificate to a holder
         evidencing the shares of Common Stock issuable to such holder upon
         conversion of such holder's shares of Series A Preferred until after
         the certificate or certificates evidencing such holder's shares of
         Series A Preferred are delivered for conversion to the Company, or the
         holder of such shares of Series A Preferred notifies the Company that
         such certificates have been lost, stolen or destroyed and such holder
         provides an affidavit, in a form reasonably satisfactory to the
         Company, to such effect. The Company shall, upon the request of any
         holder, use its best efforts to deliver any certificate or certificates
         required to be delivered by the Company under this Section 4.

                  (e) Conversion Ratio. Subject to Section 4(f), each share of
         Series A Preferred shall be convertible into that number of shares of
         Common Stock (the "Conversion Ratio") that is determined by this
         Section 4(e):

                      (i) If on the date of issuance of such share of Series A
         Preferred, the closing price of a share of Common Stock on the NASDAQ
         National Market (the "Closing Price") is greater than or equal to $6.00
         per share and less than or equal to $8.00 per share, the Conversion
         Ratio shall be the number obtained by the following formula:

                  Conversion Ratio =     2,166,666
                                       ------------
                                          100,000

                      (ii) If on the date of issuance of such share of Series A
         Preferred, the Closing Price is greater than or equal to $4.00 per
         share and less than $6.00 per share, the Conversion Ratio shall be the
         number obtained by the following formula:


                                       3


<PAGE>   4




          Conversion Ratio =  2,166,666 + [2,083 x (6.00 - Closing Price) x 100]
                             --------------------------------------------------
                                                  100,000

                      (iii) If on the date of issuance of such share of Series A
         Preferred, the Closing Price is less than $4.00 per share, the
         Conversion Ratio shall be the number obtained by the following formula:

              Conversion Ratio =                  25,000,000
                                   --------------------------------------
                                    (Closing Price) x (2.42) x (100,000)

(iv)     If on the date of issuance of such share of Series A Preferred, the
         Closing Price is greater than $8.00 per share, the Conversion Ratio
         shall be the number obtained by the following formula:

              Conversion Ratio =                  25,000,000
                                   --------------------------------------
                                    (Closing Price) x (1.44) x (100,000)

                  (f) Adjustments.

                      (i) Adjustment to Conversion Ratio for Stock Dividends and
         for Combinations or Subdivisions of Common Stock. If the Company, at
         any time or from time to time while any shares of Series A Preferred
         are outstanding, shall (A) declare or pay, without consideration, a
         stock dividend or otherwise make a distribution or distributions on
         shares of its capital stock payable in shares of Common Stock (or
         securities convertible into shares of Common Stock) or in any right to
         acquire Common Stock for no consideration; (B) effect a subdivision or
         split of the outstanding shares of Common Stock into a greater number
         of shares of Common Stock (by stock split, reclassification or
         otherwise than by payment of a dividend in Common Stock or in any right
         to acquire Common Stock); (C) combine or consolidate, by
         reclassification or otherwise, outstanding shares of Common Stock into
         a lesser number of shares or (D) issue by reclassification or exchange
         of the Common Stock any shares of capital stock of the Company, then
         the Conversion Ratio shall be multiplied by a fraction, the numerator
         of which shall be the number of shares of Common Stock outstanding
         after such event and the denominator of which shall be the number of
         shares of Common Stock outstanding before such event. Any adjustment
         made pursuant to this Section 4(f)(i) shall become effective
         immediately after the record date for the determination of stockholders
         entitled to receive such dividend or distribution and shall become
         effective immediately after the effective date in the case of a
         subdivision, combination or reclassification.

                      (ii) Adjustments for Reclassification and Reorganization.
         In case of any reclassification of the Common Stock, or any compulsory
         share exchange pursuant to which the Common Stock is converted into
         other securities, cash or property, the holders of the Series A
         Preferred then outstanding shall have the right thereafter to convert
         such shares only into the shares of stock and other securities, cash
         and property receivable upon or deemed to be held by holders of


                                       4

<PAGE>   5




         Common Stock following such reclassification or share exchange, and the
         holders of the Series A Preferred shall be entitled upon such event to
         receive such amount of securities, cash or property as a holder of the
         number of shares of Common Stock of the Company into which such shares
         of Series A Preferred could have been converted immediately prior to
         such reclassification or share exchange would have been entitled. This
         provision shall similarly apply to successive reclassifications or
         share exchanges.

                      (iii) Certificate as to Adjustments. Whenever the
         Conversion Ratio is adjusted or readjusted pursuant to Section 4(f)(i),
         or there is an adjustment or readjustment pursuant to Section 4(f)(ii),
         the Company shall promptly compute such adjustment or readjustment in
         accordance with the terms hereof and prepare and furnish to each holder
         of Series A Preferred a certificate (an "Adjustment Certificate")
         setting forth (i) such adjustment or readjustment; (ii) the Conversion
         Ratio in effect after such adjustment or readjustment and (iii) a
         detailed statement of the facts requiring such adjustment or
         readjustment. The Company shall, upon the written request at any time
         of any holder of share of Series A Preferred, furnish or cause to be
         furnished to such holder a like certificate setting forth (i) such
         adjustment and readjustment; (ii) the Conversion Price for such series
         of Preferred Stock currently in effect and (iii) the number of shares
         of Common Stock and the amount, if any, of other property that at the
         time would be received upon the conversion of a share of Series A
         Preferred Stock.

                  (g) No Impairment. The Company shall not, by amendment of its
         Restated Certificate or through any reorganization, transfer of assets,
         consolidation, merger, dissolution, issue or sale of securities or any
         other voluntary action, avoid or seek to avoid the observance or
         performance of any of the terms to be observed or performed hereunder
         by the Company, but will at all times in good faith assist in the
         carrying out of all the provisions of this Section 4 and in the taking
         of all such action as may be necessary or appropriate in order to
         protect the conversion rights of the holders of the Series A Preferred
         against impairment.

                  (h) Fractional Shares. Upon a conversion hereunder the Company
         shall not be required to issue stock certificates representing
         fractions of shares of Common Stock, but may if otherwise permitted,
         make a cash payment in respect of any final fraction of a share based
         on the Fair Market Value of a share of Common Stock at such time. If
         the Company elects not, or is unable, to make such a cash payment, the
         holder of a share of Series A Preferred shall be entitled to receive,
         in lieu of the final fraction of a share, one whole fully paid and
         nonassessable share of Common Stock. "Fair Market Value" means on any
         particular date (i) the closing price per share of Common Stock on such
         date on the NASDAQ or on any subsequent market on which the Common
         Stock is then listed or quoted, or if there is no such price on such
         date, then the closing price per share of Common Stock on the NASDAQ or
         on such subsequent market on the date nearest preceding such date; (ii)
         if the Common Stock is not then listed or quoted on the NASDAQ or on
         such subsequent market, the closing price per share of Common Stock in
         the over-the-


                                       5


<PAGE>   6




         counter market, as reported by the National Quotation Bureau
         Incorporated or similar organization or agency succeeding to its
         functions of reporting prices) at the close of business on such date;
         (iii) if the Common Stock is not then reported by the National
         Quotation Bureau Incorporated (or similar organization or agency
         succeeding to its functions of reporting prices), then the average of
         the "Pink Sheet" quotes for the relevant conversion period, as
         determined in good faith by the Company or (iv) if the Common Stock is
         not then publicly traded the fair market value of a share of Common
         Stock as determined in good faith by the Board.

                  (i) Consolidation or Merger. In case of any consolidation or
         merger of the Company with or into another person or in case of any
         sale or transfer to another person of the property of the Company as an
         entirety or substantially as an entirety, then the holders of the
         Series A Preferred then outstanding shall have the right thereafter to
         convert such shares only into the kind and amount of shares of stock
         and other securities and property receivable upon or deemed to be held
         following such consolidation, merger, sale or transfer by a holder of a
         number of shares of the Common Stock into which such shares of Series A
         Preferred might have been converted immediately prior to such
         consolidation, merger, sale or transfer. This provision shall similarly
         apply to successive consolidations, mergers, sales or transfers.

                  (j) Issue Taxes. The issuance of certificates for Common Stock
         upon conversion of Series A Preferred shall be made without charge to
         the holders thereof for any documentary stamp or similar taxes that may
         be payable in respect of the issue or delivery of such certificate;
         provided, however, that the Company shall not be required to pay any
         tax that may be payable in respect of any transfer involved in the
         issuance and delivery of any such certificate upon conversion in a name
         other than that of the holder of such shares of Series A Preferred so
         converted.

                  (k) Reservation of Stock Issuable Upon Conversion. The Company
         shall at all times reserve and keep available out of its authorized but
         unissued shares of Common Stock, solely for the purpose of effecting
         the conversion of the shares of the Series A Preferred, such number of
         its shares of Common Stock as shall from time to time be sufficient to
         effect the conversion of all outstanding shares of the Series A
         Preferred; and if at any time the number of authorized but unissued
         shares of Common Stock shall not be sufficient to effect the conversion
         of all then outstanding shares of the Series A Preferred, the Company
         shall take such corporate action as may, in the opinion of its counsel,
         be necessary to increase its authorized but unissued shares of Common
         Stock to such number of shares as shall be sufficient for such purpose,
         including engaging in efforts to obtain the requisite stockholder
         approval of any necessary amendment to the Restated Certificate. The
         Company will take all such actions as may be required to assure that
         all shares of Common Stock issuable upon conversion of Series A
         Preferred will, upon issuance, be duly authorized, legally and validly
         issued, fully paid and non-assessable and free from all liens,
         encumbrances, equities or claims.


                                       6


<PAGE>   7




                  Section 5. No Reissuance of Series A Preferred. No share or
         shares of Series A Preferred acquired by the Company by reason of
         redemption, purchase, conversion or otherwise shall be reissued.

                  Section 6. Notices. Any and all notices or other
         communications or deliveries to be provided by the holders of the
         Series A Preferred hereunder, shall be in writing and delivered
         personally, by facsimile or sent by a nationally recognized overnight
         courier service, addressed to the attention of the Chief Executive
         Officer of the Company addressed to 301 Congress Avenue, Suite 1850,
         Austin, Texas 78701, Attention: David G. Nance, Chief Executive
         Officer, or to facsimile number (512) 708-9311, or to such other
         address or facsimile number as shall be specified in writing by the
         Company for such purpose. Any and all notices or other communications
         or deliveries to be provided by the Company hereunder shall be in
         writing and delivered personally, by facsimile or sent by a nationally
         recognized overnight courier service, addressed to each holder at the
         facsimile telephone number or address of such holder appearing on the
         books of the Company, or if no such facsimile telephone number or
         address appears, at the principal place of business of the holder. Any
         notice or other communication or deliveries hereunder shall be deemed
         given and effective on the earliest of (i) the date of transmission, if
         such notice or communication is delivered via facsimile at the
         facsimile telephone number specified in this Section 6 prior to 6:30
         p.m. (New York City time); (ii) the date after the date of
         transmission, if such notice or communication is delivered via
         facsimile at the facsimile telephone number specified in this Section 6
         later than 6:30 p.m. (New York City time) on any date and earlier than
         11:59 p.m. (New York City time) on such date; (iii) upon receipt, if
         sent by a nationally recognized overnight courier service or (iv) upon
         actual receipt by the party to whom such notice is required to be
         given.

                  THIRD, that the above resolution applies to 100,000 shares of
         the Company's authorized but unissued Preferred Stock.

                                    * * * * *





                                       7



<PAGE>   8






         IN WITNESS WHEREOF, Introgen Therapeutics, Inc. has caused this
Certificate of Designations of Series A Non-Voting Convertible Preferred Stock
to be signed by the undersigned this 2nd day of July 2001.


                                       /s/ DAVID G. NANCE
                                       ---------------------------------------
                                       David G. Nance, Chief Executive Officer


                                       /s/ RODNEY VARNER
                                       ---------------------------------------
                                       Rodney Varner, Secretary






                                       8