Exhibit 4.04

                                 FX ENERGY, INC.


              DESIGNATION OF RIGHTS, PRIVILEGES, AND PREFERENCES OF
                     2003 SERIES CONVERTIBLE PREFERRED STOCK


         Pursuant to the provisions of Nevada Revised Statutes, Section 78.195,
et seq, the undersigned corporation, FX Energy, Inc. (the "Corporation"), hereby
adopts the following Designation of Rights, Privileges, and Preferences of 2003
Series Convertible Preferred Stock (the "Designation"):

         FIRST:  The name of the Corporation is FX Energy, Inc.

         SECOND: The following resolution establishing a series of preferred
stock designated as the "2003 Series Convertible Preferred Stock" consisting of
2,250,000 shares, par value $0.001, was duly adopted by the board of directors
of the Corporation on February 26, 2003, in accordance with the articles of
incorporation of the Corporation and the corporation laws of the state of
Nevada:

         RESOLVED, there is hereby created a series of preferred stock of the
Corporation to be designated as the "2003 Series Convertible Preferred Stock"
consisting of 2,250,000 shares, par value $0.001 (referred to herein as the
"Preferred Stock"), with the following powers, preferences, rights,
qualifications, limitations, and restrictions:

         1. Liquidation.

                  1.01 In the event of any voluntary or involuntary liquidation
         (whether complete or partial), dissolution, or winding up of the
         Corporation, the holders of the Preferred Stock shall be entitled to be
         paid out of the assets of the Corporation available for distribution to
         its stockholders, whether from capital, surplus, or earnings, an amount
         per share in cash equal to the original issuance price per share,
         subject to the priority distribution required respecting any issued and
         outstanding shares of any series of Preferred Stock authorized prior to
         the date hereof. No distribution shall be made on any common stock or
         other subsequent series of preferred stock of the Corporation by reason
         of any voluntary or involuntary liquidation (whether complete or
         partial), dissolution, or winding up of the Corporation unless each
         holder of any Preferred Stock shall have received all amounts to which
         such holder shall be entitled under this subsection 1.01.

                  1.02 If on any liquidation (whether complete or partial),
         dissolution, or winding up of the Corporation, the assets of the
         Corporation available for distribution to holders of Preferred Stock
         and any other stock ranking as to any such distribution on a parity
         with the Preferred Stock shall be insufficient to pay the holders of
         outstanding Preferred Stock or such other stock the full amounts to
         which they otherwise would be entitled under subsection 1.01, the
         assets of the Corporation available for distribution to holders of
         Preferred Stock or such other stock shall be distributed to them pro
         rata on the basis of the full respective preferential amounts to which
         they are entitled.

         2. Conversion.

                  2.01 Each share of Preferred Stock is convertible into one
         share of common stock and one warrant to purchase one share of common
         stock at the times, in the manner, and subject to the conditions
         provided in this section 2.

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                  2.02 Each share of Preferred Stock shall be converted
         automatically upon the effectiveness of a registration statement
         registering the resale of the common stock to be issued upon the
         conversion of the Preferred Stock and the common stock to be issued
         upon the exercise of the warrant under the Securities Act of 1933, as
         amended, or at any time following a merger or consolidation of the
         Corporation with or into an unaffiliated entity or the sale of all or
         substantially all of the assets of the Corporation to an unaffiliated
         third party, at the election of the holder on the presentation and
         surrender at the principal office of the Corporation, of the
         certificate representing the shares of Preferred Stock, duly endorsed,
         with written instructions specifying the number of shares of Preferred
         Stock to be converted and the name and address of the person to whom
         certificate(s) representing the common stock issuable on conversion are
         to be issued.

                  2.03 Each share of Preferred Stock shall be convertible into
         one share of common stock (a "Conversion Rate") and one warrant to
         purchase one share of common stock at $3.60 per share (the "Warrant
         Exercise Price"), exercisable at any time on or after midnight, March
         1, 2004, and on or before 5:00 p.m., March 1, 2008, Salt Lake City,
         Utah time, all as more particularly set forth in the form of warrant
         attached hereto as Appendix A and incorporated herein by this reference
         ("Warrant"). The date of conversion (the "Conversion Date") shall be
         the date of receipt by the Corporation of the stock certificate(s)
         representing the shares of Preferred Stock being converted with the
         conversion certificate thereon duly executed. The Corporation shall,
         within five business days after the Conversion Date, deliver or cause
         to be delivered by overnight courier a stock certificate representing
         the number of shares of common stock and, if applicable, a Warrant into
         which shares of Preferred Stock were converted in accordance herewith
         together with a certificate representing the remaining number of shares
         of Preferred Stock not being converted thereby, if any. The Conversion
         Rate and Warrant Exercise Price shall be subject to adjustment pursuant
         to subsection 2.04.

                  2.04 In order to prevent dilution of the rights granted
         hereunder, the Conversion Rate and the Warrant Exercise Price shall be
         subject to adjustment from time to time in accordance with this
         subsection 2.04.

                           (a) In the event the Corporation shall declare a
                  stock dividend or make any other distribution on any capital
                  stock of the Corporation payable in common stock, options to
                  purchase common stock, or securities convertible into common
                  stock, or the Corporation shall at any time subdivide (other
                  than by means of a dividend payable in common stock) its
                  outstanding shares of common stock into a greater number of
                  shares or combine such outstanding stock into a smaller number
                  of shares, then in each such event, the Conversion Rate and
                  Warrant Exercise Price in effect immediately prior to such
                  combination shall be adjusted so that the holders of the
                  Preferred Stock shall be entitled to receive the kind and
                  number of shares of common stock or other securities of the
                  Corporation that they would have owned or have been entitled
                  to receive, after the happening of any of the events described
                  above, had such shares of Preferred Stock been converted or
                  Warrant exercised immediately prior to the happening of such
                  event or any record date with respect thereto; an adjustment
                  made pursuant to this subsection (a) shall become effective
                  immediately after the effective date of such event retroactive
                  to the record date for such event.

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                           (b) If any capital reorganization or reclassification
                  of the capital stock of the Corporation, consolidation or
                  merger of the Corporation with another corporation, or the
                  sale of all or substantially all of its assets to another
                  corporation shall be effected in such a way that holders of
                  common stock shall be entitled to receive stock, securities,
                  or assets with respect to or in exchange for common stock,
                  then, as a condition of such reorganization, reclassification,
                  consolidation, merger, or sale, lawful adequate provisions
                  shall be made whereby the holders of the Preferred Stock shall
                  thereafter have the right to acquire and receive on conversion
                  of the Preferred Stock or Exercise of a Warrant such shares of
                  stock, securities, or assets as would have been issuable or
                  payable (as part of the reorganization, reclassification,
                  consolidation, merger, or sale) with respect to or in exchange
                  for such number of outstanding shares of common stock as would
                  have been received on conversion of the Preferred Stock
                  immediately before such reorganization, reclassification,
                  consolidation, merger, or sale. In any such case, appropriate
                  provision shall be made with respect to the rights and
                  interests of the holders of the Preferred Stock to the end
                  that the provisions hereof (including provisions for
                  adjustments of the Conversion Rate and Warrant Exercise Price
                  and for the number of shares issuable on conversion of the
                  Preferred Stock or exercise of a Warrant) shall thereafter be
                  applicable in relation to any shares of stock, securities, or
                  assets thereafter deliverable on the conversion of the
                  Preferred Stock or exercise of a Warrant. In the event of a
                  merger or consolidation of the Corporation with or into
                  another corporation, or the sale of all or substantially all
                  of its assets as a result of which a number of shares of
                  common stock of the surviving or purchasing corporation
                  greater or lesser than the number of shares of common stock
                  outstanding immediately prior to such merger, consolidation,
                  or purchase are issuable to holders of common stock, then the
                  Conversion Rate and Warrant Exercise Price in effect
                  immediately prior to such merger, consolidation, or purchase
                  shall be adjusted in the same manner as though there was a
                  subdivision or combination of the outstanding shares of common
                  stock. The Corporation will not effect any such consolidation,
                  merger, or sale unless, prior to the consummation thereof, the
                  successor corporation resulting from such consolidation or
                  merger or the corporation purchasing such assets shall assume
                  by written instrument mailed or delivered to the holders of
                  the Preferred Stock, at the last address of each such holder
                  appearing on the books of the Corporation, the obligation to
                  deliver to each such holder such shares of stock, securities,
                  or assets as, in accordance with the foregoing provisions,
                  such holder may be entitled to acquire on conversion of
                  Preferred Stock.

                           (c) No adjustment shall be made in the Conversion
                  Rate and Warrant Exercise Price of the number of shares of
                  common stock issuable on conversion of Preferred Stock or
                  exercise of a Warrant solely as a result of:

                                    (i) the offer and sale of any shares of
                           Preferred Stock, common stock, or other securities
                           convertible or exercisable into shares of common
                           stock;

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                                    (ii) the issuance of any common stock,
                           securities, or assets on conversion or redemption of
                           shares of Preferred Stock;

                                    (iii) the issuance of any shares of common
                           stock, securities, or assets on account of the
                           antidilution provisions set forth in this subsection
                           2.04, other than as heretofore provided in this
                           subsection 2.04;

                                    (iv) the purchase or other acquisition by
                           the Corporation of any capital stock, evidence of its
                           indebtedness, or other securities of the Corporation;
                           or

                                    (v) the sale or exchange by the Corporation
                           for cash or other property of any common stock,
                           evidence of its indebtedness, or other securities of
                           the Corporation, including securities containing the
                           right to subscribe for or purchase common stock or
                           Preferred Stock of the Corporation.

                  2.05 The Corporation covenants and agrees that:

                           (a) The shares of common stock, securities, or assets
                  issuable on any conversion of any shares of Preferred Stock or
                  exercise of a Warrant shall have been deemed to have been
                  issued to the person on the Conversion Date, and on the
                  Conversion Date such person shall be deemed for all purposes
                  to have become the record holder of such common stock,
                  securities, or assets.

                           (b) All shares of common stock or other securities
                  that may be issued on any conversion of the Preferred Stock
                  will, on issuance, be fully paid and nonassessable and free
                  from all taxes, liens, and charges with respect to the issue
                  thereof. Without limiting the generality of the foregoing, the
                  Corporation will from time to time take all such action as may
                  be requisite to assure that the par value of the unissued
                  common stock or other securities acquirable on any conversion
                  of the Preferred Stock is at all times sufficient to render
                  the common stock issued upon conversion as fully paid and
                  nonassessable.

                           (c) The issuance of certificates for common stock or
                  other securities on conversion of the Preferred Stock shall be
                  made without charge to the registered holder thereof for any
                  issuance tax in respect thereof or other costs incurred by the
                  Corporation in connection with the conversion of the Preferred
                  Stock and the related issuance of common stock or other
                  securities.

                           (d) The number of shares of common stock issuable
                  upon conversion of the Preferred Stock hereunder shall at all
                  times and under all circumstances be fully and validly
                  reserved from the Corporation's authorized and unissued shares
                  of common stock for issuance therefor.

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         3. Voting Rights. The Preferred Stock shall not be voted on any matter
submitted to the stockholders for consideration, except to the extent that the
consent of the holders of the Preferred Stock, voting as a class, is
specifically required by the provisions of the corporation laws of the state of
Nevada, as now existing or as hereafter amended. Notwithstanding the foregoing,
the holders of the Preferred Stock shall vote as a separate class on any
resolution proposed for adoption by the stockholders of the Corporation that
seeks to (a) authorize, create, or issue, or increase the authorized or issued
amount, of any class or series of stock ranking senior to the Preferred Stock
with respect to the payment of dividends or the distribution of assets upon
dissolution, liquidation, or winding up of the Corporation or that may be
convertible into any class of shares ranking senior to the Preferred Stock as
regards to participation in dividends or the distribution of assets on
dissolution, liquidation, or winding up; or (b) amend, alter, or repeal the
provisions of the Corporation's articles of incorporation or this Designation,
so as to adversely affect any right, preference, privilege, or voting power of
the Preferred Stock or the holders thereof. In addition, without the approval of
holders of at least a majority of the issued and outstanding shares of Preferred
Stock, the Corporation shall not become subject to any restriction on the
Preferred Stock other than restrictions arising under the general corporation
laws of the state of Nevada or existing under the articles of incorporation of
the Corporation as in effect on the date of this Designation. When entitled to
vote in accordance with the foregoing, each holder of Preferred Stock shall be
entitled to such number of votes in respect of each share of such stock held by
such holder that would be appurtenant to the common stock issuable upon
conversion in respect of such stock.

         4. Additional Provisions

                  4.01 No change in the provisions of the Preferred Stock set
         forth in this Designation affecting any interests of the holders of any
         shares of Preferred Stock shall be binding or effective unless such
         change shall have been approved or consented to by the holders of a
         majority of the Preferred Stock in the manner provided in the
         corporation laws of the state of Nevada, as the same may be amended
         from time to time.

                  4.02 A share of Preferred Stock shall be transferable only on
         the books of the Corporation maintained at its principal office, on
         delivery thereof duly endorsed by the holder or by holder's duly
         authorized attorney or representative or accompanied by proper evidence
         of succession, assignment, or authority to transfer. In all cases of
         transfer by an attorney, the original letter of attorney, duly
         approved, or an official copy thereof duly certified, shall be
         deposited and remain with the Corporation. In case of transfer by
         executors, administrators, guardians, or other legal representatives,
         duly authenticated evidence of their authority shall be produced and
         may be required to be deposited and remain with the Corporation in its
         discretion. On any registration or transfer, the Corporation shall
         deliver a new certificate representing the share of Preferred Stock so
         transferred to the person entitled thereto.

                  4.03 The Corporation shall not be required to issue any
         fractional shares of common stock or any Warrant to purchase a
         fractional share on the conversion of any share of Preferred Stock. If
         any fraction of a share of common stock or Warrant to purchase a
         fractional share would, except for the provisions of this subsection
         4.03, be issuable on the conversion of any share of Preferred Stock,
         the Corporation shall round the number of shares or Warrants to the
         nearest whole number of shares.

                  4.04 Any notice required or permitted to be given to the
         holders of the Preferred Stock under this Designation shall be deemed
         to have been duly given if mailed by first class mail, postage prepaid,
         to such holders at their respective addresses appearing on the stock
         records maintained by or for the Corporation and shall be deemed to
         have been given as of the date deposited in the United States mail.

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         IN WITNESS WHEREOF, the foregoing Designation of Rights, Privileges,
and Preferences of 2003 Convertible Preferred Stock of the Corporation has been
executed this 14th day of March, 2003.

ATTEST:                                           FX ENERGY, INC.


By /s/ Scott J. Duncan                            By /s/ David N. Pierce
   ------------------------------                    ---------------------------
   Scott J. Duncan, Secretary                        David N. Pierce, President



STATE OF UTAH                       )
                                    :ss
COUNTY OF SALT LAKE                 )

         On March 14, 2003, before me, the undersigned, a notary public in and
for the above county and state, personally appeared David N. Pierce and Scott J.
Duncan, who being by me duly sworn, did state, each for themselves, that he,
David N. Pierce, is the president, and that he, Scott J. Duncan, is the
secretary, of FX Energy, Inc., a Nevada corporation, and that the foregoing
Designation of Rights, Privileges, and Preferences of 2003 Series Convertible
Preferred Stock of FX Energy, Inc. was signed on behalf of such corporation by
authority of a resolution of its board of directors, and that the statements
contained therein are true.

         WITNESS MY HAND AND OFFICIAL SEAL.


                                                              /s/
                                                        ------------------------
                                                        Notary Public