<PAGE>

                                                                    Exhibit 4.10


                          CERTIFICATE OF DESIGNATIONS
                                      OF
                     SERIES G2 CONVERTIBLE PREFERRED STOCK
                                      OF
                           HARKEN ENERGY CORPORATION

     Harken Energy Corporation, a Delaware corporation, DOES HEREBY CERTIFY:

     That, pursuant to the authority conferred upon the Board of Directors of
said corporation by virtue of its certificate of incorporation as amended and in
accordance with Section 151 of the General Corporation Law of the State of
Delaware (the "DGCL"), said Board of Directors has duly adopted a resolution at
a special meeting of the Board of Directors held on May 30, 2001, providing for
the issuance of a series of preferred stock, par value $1.00 per share,
designated as Series G2 Convertible Preferred Stock, which resolution reads as
follows:

     "RESOLVED, that the Board of Directors (the "BOARD OF DIRECTORS") of Harken
Energy Corporation (the "CORPORATION") hereby authorizes the issuance of a
series of preferred stock and fixes its designation, powers, preferences and
relative, participating, optional or other special rights, and qualifications,
limitations and restrictions thereof, as follows:

     Section 1.  Designation.  The distinctive serial designation of said series
shall be "SERIES G2 CONVERTIBLE PREFERRED STOCK" (hereinafter called "SERIES G2
PREFERRED STOCK").  Each share of Series G2 Preferred Stock shall be identical
in all respects with all other shares of Series G2 Preferred Stock.

     Section 2.  Number of Shares.  The number of authorized shares of Series G2
Preferred Stock shall be, in aggregate, 100,000 shares.  The number of
authorized shares of Series G2 Preferred Stock may be increased or reduced by
the Board of Directors of the Corporation by the filing of a certificate
pursuant to the provisions of the DGCL stating that the change has been so
authorized.  When shares of Series G2 Preferred Stock are purchased or otherwise
acquired by the Corporation or converted into Common Stock, par value $0.01 per
share, of the Corporation (the "COMMON STOCK"), the Corporation shall take all
necessary action to cause the shares of Series G2 Preferred Stock so purchased
or acquired to be canceled and reverted to authorized but unissued shares of
Series G2 Preferred Stock undesignated as to series.

     Section 3.  Rank.  The Series G2 Preferred Stock shall, with respect to
dividend rights and rights on liquidation, winding-up and dissolution, rank (i)
junior to all claims of creditors, including holders of the Corporation's
outstanding debt securities, (ii) junior to all obligations of the Corporation's
Subsidiaries (as defined in Section 13 below), (iii) senior to all classes of
Common Stock and to each other class of preferred stock established hereafter by
the Board of Directors of the Corporation, the terms of which expressly provide
that it ranks junior to the Series G2 Preferred Stock as to dividend rights and
rights on liquidation, winding-up and dissolution of the Corporation
(collectively referred to, together with all classes of Common Stock of the
Corporation, as "JUNIOR STOCK"), and (iv) on a parity with each other class of
preferred stock established or issued hereafter by the Board of Directors of the
Corporation the terms of which expressly provide that such class or series shall
rank on a parity with the Series G2 Preferred Stock as to dividend rights and
rights on liquidation, winding-up and dissolution (collectively referred to as
"PARITY STOCK").  The Corporation may authorize the issuance of any amount of
Parity Stock (which may provide for the payment of dividends in additional
shares of Parity Stock in lieu of cash dividends) without the approval of the
holders of the Series G2 Preferred Stock.   The Series G2 Preferred Stock shall
rank as Parity Stock to the Series G1 Preferred Stock, previously authorized by
the Board.

                                       1
<PAGE>

     Section 4. Dividends.

     (a) The holders of record, as of the Record Date therefor, of the
outstanding shares of Series G2 Preferred Stock shall be entitled to receive,
when, as and if declared by the Board of Directors of the Corporation, out of
funds legally available therefor, dividends on the Series G2 Preferred Stock at
an annual rate equal to $8.00 per share (equivalent to 8% of the liquidation
preference annually), payable semi-annually in arrears in cash or, at the option
of the Corporation, in Freely Tradeable shares of the Corporation's Common
Stock. If and when the Corporation shall elect from time to time to pay such
dividends in shares of Common Stock, such shares will be valued at $3.00 per
share; provided, however, that the Corporation may elect to pay such dividends
in shares of the Corporation's Common Stock only if such shares of Common Stock
would upon issuance be Freely Tradeable (as defined in Section 13 below) by the
Corporation; and, provided further, that (i) if the outstanding shares of Common
Stock shall be subdivided into a greater number of shares of Common Stock, such
$3.00 per share valuation shall be proportionately reduced on the day upon which
such subdivision becomes effective, and (ii) if the outstanding shares of Common
Stock shall be combined into a smaller number of shares of Common Stock, such
$3.00 per share valuation shall be proportionately increased on the day such
combination becomes effective.  In case the Corporation shall take any action
affecting the Common Stock, other than the aforementioned adjustments, which in
the Board of Directors would materially adversely affect the conversion right of
the holders of the shares of Series G2 Preferred Stock, such $3.00 valuation may
be adjusted, to the extent permitted by law, in such manner, if any, and at such
time, as the Board of Directors may determine to be equitable in the
circumstances; provided, however, that in no event shall the Board of Directors
be required to take such action.

     (b) All dividends shall be cumulative, whether or not earned or declared,
and shall accrue from the date of issuance of the Series G2 Preferred Stock and
shall be payable semi-annually in arrears, when, as and if declared by the Board
of Directors.  Such dividends will be payable on December 30 and June 30 of each
year (a "DIVIDEND PAYMENT DATE"), commencing on December 31, 2001; provided,
however, that if a Dividend Payment Date is not a Stock Exchange Business Day,
then the dividend shall be payable on the first immediately succeeding Stock
Exchange Business Day.  Dividends shall be paid to the holders of record of the
Series G2 preferred Stock as their names appear on the stock transfer records of
the Corporation on the date designated by the Board of Directors ("RECORD
DATE"), provided, however, that such Record Date may not precede the date upon
which the resolution fixing the Record Date is adopted, and which Record Date
may not be more than sixty (60) days prior to the Dividend Payment Date. The
amount of the dividends payable on the Series G2 Preferred Stock for each semi-
annual dividend period shall be computed by dividing by two (2) the annual rate
per share set forth in subsection (a) above.  Dividends shall be computed on the
basis of a 360-day year of twelve 30-day months.

     (c) No dividends may be declared or paid or funds set apart for the payment
of dividends on any Parity Stock for any period unless full cumulative dividends
shall have been or contemporaneously are declared and paid in full or declared
and a sum in cash or shares of Common Stock sufficient for such payment set
apart for such payment on the Series G2 Preferred Stock except in the event of
the conversion of any such Parity Stock into Common Stock.  If full dividends
are not so paid, the Series G2 Preferred Stock shall share dividends pro rata
with the Parity Stock.  No dividends may be paid or set apart for such payment
on Junior Stock (except dividends on Junior Stock payable in additional shares
of Junior Stock) and no Junior Stock or Parity Stock may be repurchased or
otherwise retired for value nor may funds be set apart for payment with respect
thereto, if cumulative dividends have not been paid in full on the Series G2
Preferred Stock in cash or shares of Common Stock; provided, however, that the
Corporation may repurchase Junior Stock (i) in the open market from time to time
as and to the fullest extent permitted by Rule 10b-18 promulgated under the
Securities Exchange Act of 1934, as amended (240 C.F.R. ' 10b-18), or
corresponding rule from time to time in effect, and (ii) in a private purchase
or in an "issuer tender offer" as defined in Rule 13e-4 under the Exchange Act
from time to time so long as such repurchases do not exceed ten percent (10%) of
the then outstanding shares of Junior Stock.  Dividends on account of arrears
for any past dividend period may be declared and paid at any time without
reference to any regular Dividend Payment Date, to holders of record on a date
not more than forty-five (45) calendar days prior to the payment thereof, as

                                       2
<PAGE>

may be fixed by the Board of Directors of the Corporation. No interest shall be
payable with respect to any dividend payment that may be in arrears. Except as
provided above, so long as any shares of the Series G2 Preferred Stock are
outstanding, the Corporation shall not make payment on account of the purchase
or other retirement of any Parity Stock or Junior Stock, and shall not permit
any corporation or other entity directly or indirectly controlled by the
Corporation to purchase any Parity Stock, Junior Stock or any warrants, rights,
calls or options unless full cumulative dividends determined to be in accordance
herewith on the Series G2 Preferred Stock have been paid (or are deemed paid) in
full.

     (d) All dividends payable on the Series G2 Preferred Stock shall be paid
net of withholding tax, if any, under all applicable laws (including applicable
income tax treaties).  The Corporation will, subject to certain exceptions and
limitations set forth below, pay, as additional dividends, such additional
amounts (the "ADDITIONAL AMOUNTS") to the holder of any Series G2 Preferred
Stock as may be necessary in order that every net payment of the principal or
dividends on such Series G2 Preferred Stock, after withholding for or on account
of any present or future tax, duty, assessment or governmental charge imposed or
levied upon or as a result of such payment by or on behalf of the United States
(or any political subdivision, authority or agency thereof or therein having the
power to tax) (collectively, "TAXES"), will not be less than the amount such
holder would have received if such Taxes had not been withheld, provided that no
Additional Amounts will be payable with respect to a payment which is subject to
such Taxes by reason of such holder being connected with the United States (or
any political subdivision thereof) otherwise than by the mere holding of the
Series G2 Preferred Stock or the receipt of payments made under or with respect
to the Series G2 Preferred Stock.  In addition, the Corporation will indemnify
and hold harmless each holder of the Series G2 Preferred Stock (subject to the
exclusion set forth above) and will, upon written request of each holder
(subject to the exclusion set forth above), and provided that reasonable
supporting documentation is provided, reimburse each other holder for the amount
of any Taxes levied or imposed by the United States and paid by or on behalf of
the holder as a result of payments made under or with respect to the Series G2
Preferred Stock.  Any payment made pursuant to this paragraph shall be
considered and Additional Amount.  If the Corporation becomes generally subject
at any time to any taxing jurisdiction other than or in addition to the United
States, references in this Certificate of Designations to the United States
shall be read and construed as reference to the United States and/or such other
jurisdiction.

     Section 5.  Preference on Liquidation.

     (a) Upon any voluntary or involuntary liquidation, dissolution or winding-
up of the Corporation, holders of Series G2 Preferred Stock shall be entitled to
be paid, out of the assets of the Corporation available for distribution to
stockholders, the liquidation preference of $100.00 per share of Series G2
Preferred Stock, plus, without duplication, an amount in cash equal to all
accrued and unpaid dividends thereon to the date fixed for liquidation,
dissolution or winding-up (including an amount equal to a prorated dividend for
the period from the last Dividend Payment Date, or if such event is prior to the
first Dividend Payment Date, from the Closing Date, to the date fixed for
liquidation, dissolution or winding-up), before any distribution is made on any
Junior Stock, including, without limitation, any class of common stock of the
Corporation.

     (b) If, upon any voluntary or involuntary liquidation, dissolution or
winding-up of the Corporation, the amounts payable with respect to the Series G2
Preferred Stock and all Parity Stock are not paid in full, then the assets of
the Corporation available for distribution among the holders of the Series G2
Preferred Stock and any Parity Stock shall bear to each other the same ratio
that the full amounts payable on liquidation, dissolution or winding-up of the
Corporation to the holders of shares of Series G2 Preferred Stock and any Parity
Stock bear to each other.

     (c) After payment of the full amount of the liquidation preference and
accumulated and unpaid dividends to which they are entitled, the holders of
shares of Series G2 Preferred Stock shall not be entitled to any further
participation in any distribution of assets of the Corporation.

                                       3
<PAGE>

     (d) Neither the sale, conveyance, exchange or transfer (for cash, shares of
stock, securities or other consolidation) of all or substantially all of the
property or assets of the Corporation nor the consolidation or merger of the
Corporation with one or more entities shall be deemed to be or constitute a
liquidation, dissolution or winding-up of the Corporation.

     (e) Notice of any payment to the holders of Series G2 Preferred Stock as a
result of the liquidation, dissolution or winding-up of the Corporation, stating
the payment date or dates when and the place or places where the amounts
distributable in such circumstances shall be payable, shall be given not more
than sixty (60) but not less than thirty (30) days prior to any payment date
stated therein, to the holders of shares of Series G2 Preferred Stock as
provided in Section 11 herein.

     Section 6.  Voting.  The holders of Series G2 Preferred Stock shall have no
voting rights except as required by law.  In exercising any voting rights, each
outstanding share of Series G2 Preferred Stock shall be entitled to one vote.

     Section 7.  Holder Conversion Rights.

     (a) Each holder of shares of Series G2 Preferred Stock shall have the right
("CONVERSION RIGHT"), subject as provided herein and to any applicable laws and
regulations, at any time and from time to time at the holder's option to convert
each share of Series G2 Preferred Stock into shares of Common Stock at the
conversion price (subject to adjustment as described in Section 8 below) of
$3.00 per share of underlying Common Stock (the "CONVERSION PRICE") for each
$100.00 liquidation value per share of Series G2 Preferred Stock plus the amount
of any accrued and unpaid dividends (whether or not earned or declared) on the
Series G2 Preferred Stock delivered for conversion as specified herein
(including an amount equal to a prorated dividend from the immediately preceding
Dividend Payment Date to the date of such conversion, or, if such conversion is
prior to the first Dividend Payment Date, from the Closing Date to the date of
such conversion); provided, however, that the Corporation may, at its sole
discretion, pay any or all of such accrued and unpaid dividends in cash. Subject
to the provisions of the DGCL, no fractional shares of Common Stock shall be
issued upon conversions, but the number of shares shall be rounded up or down to
the nearest whole number.

     (b) If the Corporation elects to pay any accrued and unpaid dividends in
cash, the amount of any such accrued and unpaid dividends shall be promptly sent
to the holder thereof by means of check or other means provided by the
Corporation after the receipt of the notice and funds, if any, referred to in
Sections 7(d) and 7(e) below.

     (c) As promptly as practicable after the surrender of certificates for
shares of the Series G2 Preferred Stock for conversion and the receipt of the
notice and funds, if any, as described in Sections 7(d) and 7(e) below, the
Corporation shall issue and shall deliver to such holder, or on such holder's
written order, a certificate or certificates for the number of shares of Common
Stock issuable upon the conversion of such shares of the Series G2 Preferred
Stock in accordance with the provisions of this Section 7, together with
certificates representing the number of shares of Common Stock in payment of any
accrued but unpaid dividends if the Corporation elects to pay such dividends in
Common Stock.  Each conversion with respect to such shares of the Series G2
Preferred Stock shall be deemed to have been effected immediately prior to the
close of business on the date on which the certificates for shares of the Series
G2 Preferred Stock shall have been surrendered and such notice shall have been
received by the Corporation as aforesaid, and the Person or Persons entitled to
receive the Common Stock issuable upon such conversion shall be deemed for all
purposes to be the record holder or holders of such Common Stock upon that date.

                                       4
<PAGE>

     (d) In order to exercise the conversion right, the holder of each share of
Series G2 Preferred Stock to be converted shall surrender that certificate
representing such shares, duly endorsed or assigned to the Corporation or in
blank, at the office of the transfer agent for the Series G2 Preferred Stock and
shall give written notice to the Corporation in the form of Exhibit A attached
hereto.  Such notice shall also state the name or names (with address) in which
the shares of Common Stock that shall be issuable upon such conversion shall be
issued.  Each share surrendered for conversion shall, unless the shares issuable
on conversion are to be issued in the same name as the name in which such shares
of the Series G2 Preferred Stock is registered, be duly endorsed by, or
accompanied by, instruments of transfer (in each case, in form reasonably
satisfactory to the Corporation), duly executed by the holder or such holder's
duly authorized attorney-in-fact.

     (e) If a holder converts shares of the Series G2 Preferred Stock, the
Corporation shall pay any and all documentary, stamp or similar issue or
transfer tax payable in respect of the issue or delivery of the shares of the
Series G2 Preferred Stock (or any other securities issued on account thereof
pursuant hereto) or Common Stock upon the conversion; provided, however, the
Corporation shall not be required to pay any such tax that may be payable
because any such shares are issued at the request of the holder in a name other
than the name of the holder. In the event that the shares are to be issued in a
name other than that of the holder, the holder shall provide funds necessary to
pay any and all of the foregoing taxes, if any shall be applicable.

     (f) The Corporation shall reserve out of its authorized but unissued Common
Stock or its Common Stock held in treasury enough shares of Common Stock to
permit the conversion of all of the outstanding shares of the Series G2
Preferred Stock, but in no event shall the Corporation be required to reserve
sufficient shares of Common Stock to permit the conversion of any accrued and
unpaid dividends on the Series G2 Preferred Stock.  The Corporation shall from
time to time, in accordance with the DGCL, increase the authorized amount of its
Common Stock if at any time the authorized amount of its Common Stock remaining
unissued shall not be sufficient to permit the conversion of all shares of the
Series G2 Preferred Stock at the time outstanding.  If any shares of Common
Stock required to be reserved for issuance upon conversion of shares of the
Series G2 Preferred Stock hereunder require registration with or approval of any
governmental authority under any federal or state law before the shares may be
issued upon conversion, the Corporation shall in good faith and as expeditiously
as possible endeavor to cause the shares to be so registered or approved.  All
shares of Common Stock delivered upon conversion of the shares of the Series G2
Preferred Stock will, upon delivery, be duly authorized and validly issued,
fully paid and nonassessable, free from all taxes, liens and charges with
respect to the issue thereof.

     Section 8.  Conversion Price Adjustments.

     (a) Subdivision of Common Stock. In case outstanding shares of Common Stock
shall be subdivided into a greater number of shares of Common Stock, the
Conversion Price in effect at the opening of business on the day following the
day upon which such subdivision becomes effective shall be proportionately
reduced, and, conversely, in case outstanding shares of Common Stock shall each
be combined into a smaller number of shares of Common Stock, the Conversion
Price in effect at the opening of business on the day following the day upon
which such combination becomes effective shall be proportionately increased,
such reduction or increase, as the case may be, to become effective immediately
after the opening of business on the day following the day upon which such
subdivision or combination becomes effective.

     (b) Certificate of Adjustment and Notice.  Whenever the Conversion Price is
adjusted as herein provided, the Corporation shall promptly file with the
transfer agent for the Series G2 Preferred Stock a certificate of an officer of
the Corporation setting forth the Conversion Price after the adjustment and
setting forth a brief statement of the facts requiring such adjustment and a
computation thereof. The Corporation shall promptly cause a notice of the
adjusted Conversion Price be given to the holders of shares of the Series G2
Preferred Stock as provided in Section 11 herein.

                                       5
<PAGE>

     (c) Adjustment in Conversion Price in Case of Certain Events.  In case the
Corporation shall take any action affecting the Common Stock, other than actions
described in Section 7 or this Section 8, which in the opinion of the Board of
Directors would materially adversely affect the conversion right of the holders
of the shares of the Series G2 Preferred Stock, the Conversion Price may be
adjusted, to the extent permitted by law, in such manner, if any, and at such
time, as the Board of Directors may determine to be equitable in the
circumstances; provided, however, that in no event shall the Board of Directors
be required to take any such action.

     (d) Registration of Conversion Shares.  Following receipt by the
Corporation of the first notice of conversion from a holder of Series G2
Preferred Stock, the Corporation shall file a registration statement on Form S-3
(or such other form as the Corporation may determine is appropriate) with
respect to all the Common Stock that may be issuable at any time upon the
conversion or redemption of any of the Series G2 Preferred Stock ("CONVERSION
SHARES") at the earliest practicable date, but in any event prior to 90 days
following the receipt by the Corporation of the first notice of conversion from
a holder of Series G2 Preferred Stock.  The Corporation shall use its best
efforts to cause the Commission to declare such registration statement (and any
necessary amendments thereto) effective.  The Corporation shall also use its
best efforts to maintain the effectiveness of such registration statement, and
to refile such a registration statement from time to time in the event its
effectiveness lapses, until all Conversion Shares either issued or that may be
issued are Freely Tradeable (as defined in Section 13 below) in the United
States.

     Section 9. Mandatory Conversion by Corporation.

     (a) At any time after the earlier of (i) the registration statement
referred to in subsection (d) above has been declared effective, or (ii) the
Conversion Shares are Freely Tradeable, the Corporation may, at its option,
cause all of the outstanding Series G2 Preferred Stock to be converted into
shares of Common Stock, in accordance with Section 9(b), at any time and from
time to time, if the average of the Market Prices of the Common Stock over the
Stock Exchange Business Days in any twenty (20) consecutive calendar day period
ending not more than five (5) days prior to the giving of the notice referred to
below equaled or exceeded $3.75.

     Notwithstanding the preceding,  if the outstanding shares of Common Stock
shall be subdivided into a greater number of shares of Common Stock or if the
outstanding shares of Common Stock shall be combined into a smaller number of
shares of Common Stock, such $3.75 amount shall be proportionately adjusted on
the day such combination becomes effective.  In case the Corporation shall take
any action affecting the Common Stock, other than the aforementioned
adjustments, which in the Board of Directors would materially adversely affect
the conversion right of the holders of the shares of Series G2 Preferred Stock,
such $3.75 valuation may be adjusted, to the extent permitted by law, in such
manner, if any, and at such time, as the Board of Directors may determine to be
equitable in the circumstances; provided, however, that in no event shall the
Board of Directors be required to take such action.

     (b) Each share of Series G2 Preferred Stock shall be converted into a
number of shares of Common Stock equal to: (x) each $100.00 liquidation value
per share of Series G2 Preferred Stock plus the amount of any accrued and unpaid
dividends (whether or not earned or declared) on the Series G2 Preferred Stock
(including an amount equal to a prorated dividend from the immediately preceding
Dividend Payment Date, or if such conversion is prior to the first Dividend
Payment Date, from the Closing Date, to the date of such conversion) divided by
(y) the Conversion Price.

     Notwithstanding the preceding, the Corporation may, at its sole discretion,
pay any or all of the accrued and unpaid dividends in cash. Subject to the
provisions of the DGCL, no fractional shares of Common Stock shall be issued the
optional conversion, but the number of shares shall be rounded up or down to the
nearest whole number.  The amount of any accrued and unpaid dividends that the
Corporation elects to pay in cash shall be promptly sent to the holder thereof
by means of check or other means provided by the Corporation.

                                       6
<PAGE>

     (c) The Corporation shall give thirty (30) days notice as provided in
Section 11 hereof of its intent to convert in accordance with this Section 9 no
later than thirty (30) calendar days from the end of the twenty (20) day period
described above.  Upon the giving of the notice referred to above, the
Corporation shall be bound to convert the Series G2 Preferred Stock as to which
notice has been provided.  During the 30 day notice period, holders of the
Series G2 Preferred Stock will retain their right to convert their shares of
Series G2 Preferred Stock in accordance with Section 7 above.

      Section 10.  Optional Redemption by Corporation.

     (a) Optional Redemption. In addition to its right to redeem the Series G2
Preferred Stock as provided in Section 9 above, the Corporation shall have the
option to redeem the Series G2 Preferred Stock in whole or in part in cash at
any time, and from time to time, unless the holder thereof shall have converted
such stock into Common Stock pursuant to Section 7 prior to the date of
redemption hereof, at a redemption price ("REDEMPTION PRICE") equal to (i)
$100.00 per share and (ii) accrued and unpaid dividends (whether or not
declared), such dividends being payable in cash or Freely Tradeable Common Stock
(including an amount equal to a prorated dividend from the immediately preceding
Dividend Payment Date, or if such conversion is prior to the first Dividend
Payment Date, from the Closing Date, to the redemption date).

     (b)  Procedures for Redemption.

          (i) In case of redemption of less than all shares of Series G2
     Preferred Stock at the time outstanding, the shares to be redeemed shall be
     selected pro rata, at random, or by lot or a method that complies with the
     requirements of any national stock exchange on which Series G2 Preferred
     Stock is listed as determined by the Board of Directors in its sole
     discretion.

          (ii) Notice of any redemption shall be given as provided in Section 11
     by or on behalf of the Corporation not more less than thirty (30) days
     prior to the date of redemption hereof; provided, however, that such notice
     of redemption may be a conditional notice of redemption which may condition
     the redemption upon making the redemption subject to the prior conversion
     of the Series G2 Preferred Stock before the redemption date; and provided
     further, that no failure to give such notice or any defect therein or in
     the transmission or mailing thereof shall affect the validity of the
     proceedings for the redemption of any shares of Series G2 Preferred Stock
     except as to the holder to whom the Corporation has failed to give notice
     or except as to the holder to whom notice was defective.  In addition to
     any information required by law, such notice shall state:  such redemption
     is being made pursuant to the optional redemption provisions hereof; the
     date of redemption; the Redemption Price; the number of shares of Series G2
     Preferred Stock to be redeemed and, if less than all shares held by such
     holder are to be redeemed; the number of such shares to be redeemed; the
     place or places where certificates for such issued shares are to be
     surrendered for payment of the Redemption Price; and that dividends on the
     shares to be redeemed shall cease to accrue on the date of redemption.
     Upon the expiry of the notice so given, except with respect to the
     conditions specified above, the Corporation shall become obligated to
     redeem at the time of redemption specified thereon all shares called for
     redemption.

          (iii)  If notice has been given in accordance with Section 10(b)(ii)
     above and provided that on or before the date of redemption specified in
     such notice, all funds necessary for such redemption shall have been set
     aside by the Corporation, separate and apart from its other funds in trust
     for the pro rata benefit of the holders of the shares so called for
     redemption, so as to be, and to continue to be available therefor, then,
     from and after the date of redemption,

                                       7
<PAGE>

     dividends on the shares of the Series G2 Preferred Stock so called for
     redemption shall cease to accrue, and said shares shall no longer be deemed
     to be outstanding and shall not have the status of shares of Series G2
     Preferred Stock, and all rights of the holders thereof as shareholders of
     the Corporation (except the right to receive from the Corporation the
     Redemption Price) shall cease. Upon surrender, in accordance with said
     notice, of the certificates for any issued shares so redeemed (properly
     endorsed or assigned for transfer, if the Corporation shall so require and
     the notice shall so state), such shares shall be redeemed by the
     Corporation at the Redemption Price by mailing a check to such holder's
     last registered address listed on the stock transfer records of the
     Corporation, or as otherwise agreed by the holders of Series G2 Preferred
     Stock and the Corporation. In case fewer than all the shares represented by
     any such certificate are redeemed, a new certificate or certificates shall
     be issued representing the unredeemed shares without cost to the holder
     thereof.

          (iv) Any funds deposited with a bank or trust corporation for the
     purpose of redeeming Series G2 Preferred Stock shall be irrevocable except
     that:  the Corporation shall be entitled to receive from such bank or trust
     company the interest or other earnings, if any, earned on any money so
     deposited in trust, and the holders of any shares redeemed shall have no
     claim to such interest or other earnings; and any balance of monies so
     deposited by the Corporation and unclaimed by the holders of the Series G2
     Preferred Stock entitled thereto at the expiration of two years from the
     applicable date of redemption shall be repaid, together with any interest
     or other earnings earned thereon, to the Corporation, and after any such
     repayment, the holders of the shares entitled to the funds so repaid to the
     Corporation shall look only to the Corporation for payment without interest
     or other earnings.

          (v) No Series G2 Preferred Stock may be redeemed except with funds
     legally available for the payment of the Redemption Price.

          (vi) Holders of Series G2 Preferred Stock shall retain the conversion
     rights described in Section 7 hereof until the date of any redemption of
     the shares of Series G2 Preferred Stock in accordance with this Section 10.

     (c)        Redemption by Conversion. In addition to the rights of
conversion pursuant to Section 9 hereof, on or after June 1, 2004, the
Corporation may further elect, in any six (6) month period, to redeem up to 50%
of the outstanding Series G2 Preferred Stock in accordance with this Section
10(c) by requiring their redemption on thirty (30) days notice pursuant to the
terms of this Section 10(c) (the "REDEMPTION BY CONVERSION OPTION"). The
redemption price for purposes of this Section 10(c) shall be equal to the
average Market Price of the Common Stock during the twenty (20) consecutive
Stock Exchange Business Days ending not more than five (5) Stock Exchange
Business days prior to the date notice is given by the Corporation concerning
its exercise of this Redemption by Conversion Option, subject to appropriate
adjustments to account for the effects of dividends, distributions, stock
splits, recapitalizations and similar events. If the Market Capitalization of
the Corporation is less than $300 million on the date the notice by the
Corporation of its exercise of this Redemption by Conversion Option is given,
then each share of Series G2 Preferred Stock will be redeemed for the number of
shares of Common Stock equal to 110% of the $100.00 liquidation value per share
(the "REDEMPTION VALUE") divided by the redemption price.  If the Market
Capitalization of the Corporation is $300 million or more on the date the notice
by the Corporation of its exercise of this Redemption by Conversion Option is
given, then each share of Series G2 Preferred Stock will be redeemed for the
number of shares of Common Stock equal to 105% of the Redemption Value divided
by the redemption price. The amount of the accrued and unpaid dividends (whether
or not earned or declared) accrued by the Series G2 Preferred Stock delivered
for redemption as specified above (computed to the end of the day the Series G2
Preferred Stock is so redeemed) shall be sent to the holder thereof by means of
check or other means established by the Corporation, if the dividend is in cash,
or if the dividend is in

                                       8
<PAGE>

shares of Common Stock, each as determined by the Corporation, by such means as
selected by the Corporation. All Common Stock issued pursuant to the Redemption
by Conversion Option shall be Freely Tradeable.

       Section 11.   Notice.  Where this Certificate of Designations provides
for notice of any event to the holders of the Series G2 Preferred Stock by the
Corporation or any other Person, such notice shall be sufficiently given (unless
otherwise herein specifically provided) if published in the Authorized
Newspapers.

       Section 12.    General Provisions Relating to the Series G2 Preferred
Stock.

      (a) Form.  The Series G2 Preferred Stock shall be issued in fully
registered form in the form satisfactory to the Corporation.

      (b) Compliance with United States Securities Laws.  Nothing contained
herein shall be deemed to authorize any transfers of certificates of the Series
G2 Preferred Stock otherwise than in accordance with the Securities Act.
Neither the Corporation or its transfer agent shall recognize or give effect to
any attempt to transfer (by book entry or otherwise) or convert any Series G2
Preferred Stock or any interest therein in violation of either the Securities
Act.  The certificates representing the Series G2 Preferred Stock and the
Conversion shares shall bear restrictive legends thereon recommended by legal
counsel for the Corporation regarding the restrictions on the transferability
thereof  to ensure compliance the Securities Act until the Series G2 Preferred
Stock and/or the Conversion Shares, as the case may be become Freely Tradeable.

     Section 13.  Certain Definitions.

     "Alternative Stock Exchange" means any other national or regional stock
exchange or quotation service such as the Nasdaq Market System or any similar
quotation service maintained by the National Quotation Bureau or any successor
thereto.

     "Authorized Newspapers" means the Luxembourg Wort of Luxembourg and The
Financial Times (European Edition) of London, England.  If either such newspaper
shall cease to be published, the Corporation shall substitute for it another
newspaper in Europe, customarily published at least once a day for at least five
(5) days in each calendar week, of general circulation.  If, because of
temporary suspension of publication or general circulation of either such
newspaper or for any other reason, it is impossible or, in the opinion of the
Corporation, impracticable to make any publication of any notice required by
this Certificate of Designations in the manner herein provided, such publication
or other notice in lieu thereof which is made by the Corporation in the exercise
of its reasonable discretion shall constitute a sufficient publication of such
notice.

     "Capital Stock" of any Person means the Common Stock or preferred stock of
such Person. Unless otherwise stated herein or the context otherwise requires,
"Capital Stock" means Capital Stock of the Corporation

     "Closing Date" means the date of which the Series G2 Preferred Stock is
sold to the holders thereof.

     "Commission" means the Securities and Exchange Commission.

     "Conversion Agent" means any Person (including the Corporation acting as
Conversion Agent) authorized by the Corporation to effect conversions of the
Series G2 Preferred Stock on behalf of the Corporation.

     "Dividend Payment Date" has the meaning given to it in Section 4(b) hereof.

     "Freely Tradeable" means, with respect to the Common Stock issuable upon
the conversion of or the payment of a dividend upon the Series G2 Preferred
Stock, that under the Securities Act the holders thereof may

                                       9
<PAGE>

then offer and sell any amount of such outstanding securities to the public in
the United States in transactions that are not brokers' transactions (as defined
in the Securities Act) either (i) pursuant to an effective registration
statement then in effect or (ii) pursuant to Rule 144(k). For purposes of
determining whether such securities are Freely Tradeable, it shall be assumed
that no affiliate of the issuer has ever held such securities from and after
their issuance.

     "Group" means the Corporation and all its Principal Subsidiaries.

     "Market Capitalization" means, on any date, the average, over the thirty
(30) calendar day period commencing thirty-five (35) calendar days prior to such
date, of the product of the Market Price of the Common Stock and the number of
shares of Common Stock of the Corporation issued and outstanding on such date;
provided, however, that appropriate adjustments shall be made to the Market
Prices and number of shares used in determining such Market Capitalization to
account fairly for the effect of dividends payable in equity securities of the
Corporation or any other Person, spin-offs of subsidiaries, mergers in which the
Corporation or a Principal Subsidiary is a constituent party, and similar
events.

     "Market Price" means the closing sales price on the American Stock Exchange
or any Alternative Stock Exchange on any Stock Exchange Business Day.

     "Person" means any individual, corporation, partnership, association, trust
or other entity or organization, including a government or political subdivision
or any agency or instrumentality thereof.

     "Principal Subsidiary" means a Subsidiary of either the Corporation or any
Principal Subsidiary:

     (a)   whose gross assets represent 10 percent or more of the consolidated
gross assets of the Group as calculated by reference to the then latest audited
financial statements of the Group;  or

     (b)   to which is transferred all or substantially all of the business,
undertaking and assets of a Subsidiary of the Corporation which immediately
prior to such transfer is a Principal Subsidiary, whereupon the transferor
Subsidiary shall immediately cease to be a Principal Subsidiary and the
transferee Subsidiary shall cease to be a Principal Subsidiary under the
provisions of this sub-paragraph (b) (but without prejudice to the provisions of
sub-paragraph (a) above), upon publication of its next audited financial
statements.

     "Property" means any kind of property or asset, whether real, personal,
mixed, or tangible or intangible, and any interest therein.

     "Securities Act" means the United States Securities Act of 1933 as in
effect on the date of the filing of this Certificate with the Secretary of State
of Delaware or as such act may hereafter be amended.

     "Series G2 Preferred Stock" means the Corporation's Series G2 Convertible
Preferred Stock, $1.00 par value.

     "Stock Exchange Business Day" means any day (other than a Saturday or
Sunday) on which the American Stock Exchange or the Alternative Stock Exchange,
as the case may be, is open for business.

     "Subsidiary" of any Person means any Corporation of which at least a
majority of the shares of stock having by the terms thereof ordinary voting
power to elect a majority of the Board of Directors of such Corporation
(irrespective of whether or not at the time stock of any other class or classes
of such Corporation shall have voting power by reason of the happening of any
contingency) is directly or indirectly owned or controlled by any one of or any
combinations of the Corporation or one or more of its Subsidiaries."

                                      10
<PAGE>

     IN WITNESS WHEREOF, the Corporation has caused this Certificate to be duly
executed on its behalf by its undersigned Secretary this 20th day of July, 2001.


                                    HARKEN ENERGY CORPORATION,
                                    a Delaware corporation



                                    By:  /s/ Larry E. Cummings
                                       -----------------------
                                    Name:  Larry E. Cummings
                                    Title:  Secretary

                                      11
<PAGE>

                                   EXHIBIT A

                             NOTICE OF CONVERSION

To:  Harken Energy Corporation

To:  [Conversion Agent]

          The undersigned holder of the Series G2 Convertible Preferred Stock,
par value U.S. $1.00 (the "PREFERRED STOCK") of Harken Energy Corporation (the
"CORPORATION") in the aggregate liquidation preference value of U.S. $100.00
irrevocably exercises the option to convert [INSERT NUMBER] shares of Preferred
Stock into shares of Common Stock of the Corporation, par value U.S. $0.01 (the
"COMMON STOCK"), in accordance with the terms of the Certificate of Designations
relating to the issuance by the Corporation of the Preferred Stock and directs
that the Common Stock issuable and deliverable upon such conversion be issued
and delivered to the undersigned in the name and at the address set forth below.

          If the Common Stock is not Freely Tradeable at the date hereof, the
undersigned holder hereby certifies to the Corporation that it:

          (1)(a) is an "accredited investor" (as defined in Rule 501 of
Regulation D under the U.S. Securities Act of 1933, as amended (the "SECURITIES
ACT")), or  (b) is acquiring the Common Stock in a transaction exempt from the
registration requirements of the Securities Act; and

          (2) acknowledges that the Common Stock has not been registered under
the Securities Act and are "restricted securities" within the meaning of the
Securities Act; and

          (3) understands and agrees that if within two years after the date of
the original issuance of the Preferred Stock or within three months after it
ceases to be an affiliate (within the meaning of Rule 144 under the Securities
Act) of the Corporation, upon conversion thereof the Common Stock may be resold,
pledged, or transferred only (i) to the Corporation, (ii) pursuant to an
exemption from the registration requirements of the Securities Act provided by
Rule 144 (if applicable) under the Securities Act, or (iii) pursuant to an
effective registration statement under the Securities Act, in each case in
accordance with any applicable securities law of any state of the United States;
and

          (4) it understands that the certificates representing the Common Stock
will bear a restrictive legend describing the foregoing restriction on transfer,
unless otherwise agreed by the Corporation.

          If the Common Stock is to be issued in the name of a person other than
the undersigned or a nominee of the undersigned, the undersigned will pay all
transfer taxes payable with respect thereto and is delivering herewith a
certificate in proper form that the applicable restrictions on transfer have
been complied with.

          All terms not otherwise defined herein shall have the respective
meanings set forth in the Certificate of Designations relating to the Preferred
Stock.

                                    * * * *

                                       1
<PAGE>

DATE:
     --------------------           --------------------------------
                                    Name of Holder


                                   --------------------------------
                                   Signature(s) of Holder

Address for Delivery of Shares:    --------------------------------
                                   --------------------------------
                                   --------------------------------
                                   --------------------------------

Name for Registration of Shares
 (if different than Holder):       --------------------------------