POINT THERAPEUTICS, INC.

Exhibit 1.4

THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE BEEN ACQUIRED FOR INVESTMENT AND HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY STATE SECURITIES LAW. SUCH SECURITIES MAY NOT BE SOLD OR TRANSFERRED IN THE ABSENCE OF SUCH REGISTRATION OR UNLESS SUCH SALE OR TRANSFER IS EXEMPT FROM THE REGISTRATION AND PROSPECTUS DELIVERY REQUIREMENTS OF SAID ACT AND APPLICABLE STATE SECURITIES LAWS, SUPPORTED BY AN OPINION OF COUNSEL THAT SUCH REGISTRATION IS NOT REQUIRED.

POINT THERAPEUTICS, INC.

Warrant for the Purchase of Shares of

Common Stock

FOR VALUE RECEIVED, POINT THERAPEUTICS, INC., a Delaware corporation (the “Company”), hereby certifies that Paramount Capital, Inc., its designee or its permitted assigns is entitled to purchase from the Company, at any time or from time to time commencing on March     , 2004 and prior to 5:00 P.M., New York City time, on September            , 2008,                      fully paid and non-assessable shares of common stock, $.01 par value per share, of the Company for an aggregate purchase price of [            ] ($            ). (Hereinafter, (i) said common stock, $.01 par value per share, of the Company, is referred to as the “Common Stock”; (ii) the shares of the Common Stock purchasable hereunder or under any other Warrant (as hereinafter defined) are referred to as the “Warrant Shares”; (iii) the aggregate purchase price payable for the Warrant Shares purchasable hereunder is referred to as the “Aggregate Warrant Price”; (iv) the price payable (initially $             per share subject to adjustment) for each of the Warrant Shares hereunder is referred to as the “Per Share Warrant Price”; (v) this Warrant, all similar Warrants issued on the date hereof and all warrants hereafter issued in exchange or substitution for this Warrant or such similar Warrants are referred to as the “Warrants”; (vi) the holder of this Warrant is referred to as the “Holder” and the holder of this Warrant and all other Warrants and Warrant Shares are referred to as the “Holders” and Holders of more than fifty percent (50%) of the outstanding Warrant Shares are referred to as the “Majority of the Holders”); and (vii) the then Current Market Price per share of the Common Stock (the “Current Market Price”) shall be deemed to be the last reported sale price of the Common Stock on the Trading Day immediately prior to such date or, in case no such reported sales take place on such day, the average of the last reported bid and asked prices of the Common Stock on such day, in either case on the principal national securities exchange on which the Common Stock is admitted to trading or listed, or if not listed or admitted to trading on any such exchange, the representative closing sale price of the Common Stock as reported by the National Association of Securities Dealers, Inc. Automated Quotations System (“NASDAQ”), or other similar organization if NASDAQ is no longer reporting such information, or, if the Common Stock is not reported on NASDAQ, the per share sale price for the Common Stock in the over-the-counter market as reported by the National Quotation Bureau or similar organization, or if not so available, the fair market value of the Common Stock as determined in good faith by the Board of Directors. A “Trading Day” shall mean any day on which shares of the Company’s Common Stock are sold on the respective exchange. The Aggregate Warrant Price is not subject to adjustment. The Per Share Warrant Price is subject to adjustment as hereinafter provided; in the event of any such adjustment, the number of Warrant Shares deliverable upon exercise of this Warrant shall be adjusted by dividing the Aggregate Warrant Price by the Per Share Warrant Price in effect immediately after such adjustment.

This Warrant, together with warrants of like tenor, constituting in the aggregate Warrants to purchase [            ] Warrant Shares, was originally issued pursuant to an Engagement Agreement (the “Engagement Agreement”) between the Company and Paramount Capital, Inc. in connection with a private placement by the Company of its securities.

1. Exercise of Warrant.

(a) This Warrant may be exercised in whole at any time, or in part from time to time, commencing on March    , 2004 and prior to 5:00 P.M., New York City time, on September    , 2008 by the Holder:

(i) by the surrender of this Warrant (with the subscription form at the end hereof duly executed) at the address set forth in Section 9(a) hereof, together with proper payment of the Aggregate Warrant Price, or the proportionate part thereof if this Warrant is exercised in part, with payment for the Warrant Shares made by certified or official bank check payable to the order of the Company; or

(ii) by the surrender of this Warrant (with the cashless exercise form at the end hereof duly executed) (a “Cashless Exercise”) at the address set forth in Section 9(a) hereof. Such presentation and surrender shall be deemed a waiver of the Holder’s obligation to pay the Aggregate Warrant Price, or the proportionate part thereof if this Warrant is exercised in part. In the event of a Cashless Exercise, the Holder shall exchange its Warrant for that number of Warrant Shares subject to such Cashless Exercise multiplied by a fraction, the numerator of which shall be the difference between the then Current Market Price and the Per Share Warrant Price, and the denominator of which shall be the then Current Market Price. For purposes of any computation under this Section 1(a), the then Current Market Price shall be based on the Trading Day immediately preceding such Cashless Exercise.

(b) If this Warrant is exercised in part, this Warrant must be exercised for a number of whole shares of the Common Stock and the Holder is entitled to receive a new Warrant covering the Warrant Shares that have not been exercised and setting forth the proportionate part of the Aggregate Warrant Price applicable to such Warrant Shares. Upon surrender of this Warrant, the Company will (i) issue a certificate or certificates in the name of the Holder for the largest number of whole shares of the Common Stock to which the Holder shall be entitled and, if this Warrant is exercised in whole, in lieu of any fractional share of the Common Stock to which the Holder shall be entitled, pay to the Holder cash in an amount equal to the fair value of such fractional share (determined in such reasonable manner as the Board of Directors of the Company shall determine), and (ii) deliver the other securities and properties receivable upon the exercise of this Warrant, or the proportionate part thereof, if this Warrant is exercised in part, pursuant to the provisions of this Warrant.

2. Reservation of Warrant Shares; Listing.

The Company agrees that, prior to the expiration of this Warrant, the Company shall at all times (a) have authorized and in reserve, and shall keep available, solely for issuance and delivery upon the exercise of this Warrant, the shares of the Common Stock and other securities and properties as from time to time shall be receivable upon the exercise of this Warrant, free and clear of all restrictions on sale or transfer, other than under Federal or state securities laws, and free and clear of all preemptive rights and rights of first refusal and (b) if the

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Company hereafter lists its Common Stock on any national securities exchange, the Nasdaq National Market or the Nasdaq Smallcap Market, use its best efforts to keep the Warrant Shares authorized for listing on such exchange upon notice of issuance.

3. Protection Against Dilution.

(a) If, at any time or from time to time after the date of this Warrant, the Company shall issue or distribute to the holders of shares of Common Stock evidence of its indebtedness, any other securities of the Company or any cash, property or other assets (excluding a subdivision, combination or reclassification, or dividend or distribution payable in shares of Common Stock, referred to in Section 3(b), and also excluding cash dividends or cash distributions paid out of net profits legally available therefor (any such non-excluded event being herein called a “Special Dividend”)), the Per Share Warrant Price shall be adjusted by multiplying the Per Share Warrant Price then in effect by a fraction, the numerator of which shall be the then Current Market Price in effect on the record date of such issuance or distribution less the fair market value (as determined in good faith by the Company’s Board of Directors) of the evidence of indebtedness, cash, securities or property, or other assets issued or distributed in such Special Dividend applicable to one share of Common Stock and the denominator of which shall be the then Current Market Price in effect on the record date of such issuance or distribution. An adjustment made pursuant to this Subsection 3(a) shall become effective immediately after the record date of any such Special Dividend and shall result in a corresponding adjustment to the number of Warrant Shares issuable upon exercise of this Warrant.

(b) In case the Company shall hereafter (i) pay a dividend or make a distribution on its capital stock in shares of Common Stock, (ii) subdivide its outstanding shares of Common Stock into a greater number of shares, (iii) combine its outstanding shares of Common Stock into a smaller number of shares or (iv) issue by reclassification of its Common Stock any shares of capital stock of the Company, the Per Share Warrant Price shall be adjusted to be equal to a fraction, the numerator of which shall be the Aggregate Warrant Price and the denominator of which shall be the number of shares of Common Stock or other capital stock of the Company that the Holder would have owned immediately following such action had such Warrant been exercised immediately prior thereto. An adjustment made pursuant to this Subsection 3(b) shall become effective immediately after the record date in the case of a dividend or distribution, and shall become effective immediately after the effective date in the case of a subdivision, combination or reclassification, and shall result in a corresponding adjustment to the number of Warrant Shares issuable upon exercise of this Warrant..

(c) Except as provided in Subsections 3(a) and 3(d), in case the Company shall hereafter issue or sell any Common Stock, any securities convertible into Common Stock, any rights, options or warrants to purchase or otherwise receive issuances of Common Stock or any securities convertible into, or exercisable or exchangeable for, Common Stock, in each case for a price per share or entitling the holders thereof to purchase Common Stock at a price per share (determined by dividing (i) the total amount, if any, received or receivable by the Company in consideration of the issuance or sale of such securities plus the total consideration, if any, payable to the Company upon exercise thereof (the “Total Consideration”) by (ii) the number of additional shares of Common Stock issued, sold or issueable upon exercise of such securities) that is less than the Per Share Warrant Price in effect on the date of such issuance or sale, then the Per Share Warrant Price shall be adjusted as of the date of such issuance or sale by multiplying the Per Share Warrant Price then in effect by a fraction, the numerator of which shall be (x) the sum of (A) the number of shares of Common Stock outstanding on the record date of such issuance or sale (calculated on a fully diluted basis as if all securities exercisable, convertible or exchangeable for Common Stock have been so exercised, converted or

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exchanged) plus (B) the Total Consideration divided by the current Per Share Warrant Price, and the denominator of which shall be (y) the number of shares of Common Stock outstanding on the record date of such issuance or sale (calculated on a fully diluted basis as if all securities exercisable, convertible or exchangeable for Common Stock have been so exercised, converted or exchanged) plus the maximum number of additional shares of Common Stock issued, sold or issueable upon exercise or conversion of such securities.

(d) No adjustment in the Per Share Warrant Price shall be required in the case of the issuance by the Company of Common Stock or other convertible securities (i) pursuant to any stock options, warrants or other convertible securities currently outstanding; (ii) stock options, warrants or other convertible securities issued after the date hereof, which may be approved by the Company’s Board of Directors pursuant to any Company benefit plan or exercised under any employee benefit plan of the Company to officers, directors, consultants or employees, but only with respect to such warrants or stock options as are exercisable at prices no lower than the closing price of the Common Stock as of the date of grant thereof; or (iii) upon the issuance of Common Stock pursuant to the Warrants or subscription agreement (the “Subscription Agreement”).

(e) In case of any capital reorganization or reclassification, or any consolidation or merger to which the Company is a party other than a merger or consolidation in which the Company is the continuing corporation, or in case of any sale or conveyance to another entity of the property of the Company as an entirety or substantially as an entirety, or in the case of any statutory exchange of securities with another corporation (including any exchange effected in connection with a merger of a third corporation into the Company), the Holder of this Warrant shall have the right thereafter to receive on the exercise of this Warrant the kind and amount of securities, cash or other property which the Holder would have owned or have been entitled to receive immediately after such reorganization, reclassification, consolidation, merger, statutory exchange, sale or conveyance had this Warrant been exercised immediately prior to the effective date of such reorganization, reclassification, consolidation, merger, statutory exchange, sale or conveyance and in any such case, if necessary, appropriate adjustment shall be made in the application of the provisions set forth in this Section 3 with respect to the rights and interests thereafter of the Holder of this Warrant to the end that the provisions set forth in this Section 3 shall thereafter correspondingly be made applicable, as nearly as may reasonably be, in relation to any shares of stock or other securities or property thereafter deliverable on the exercise of this Warrant. The above provisions of this Section 3(e) shall similarly apply to successive reorganizations, reclassifications, consolidations, mergers, statutory exchanges, sales or conveyances. The Company shall require the issuer of any shares of stock or other securities or property thereafter deliverable on the exercise of this Warrant to be responsible for all of the agreements and obligations of the Company hereunder. Notice of any such reorganization, reclassification, consolidation, merger, statutory exchange, sale or conveyance and of said provisions so proposed to be made, shall be mailed to the Holders of the Warrants not less than thirty (30) days prior to such event. A sale of all or substantially all of the assets of the Company for a consideration consisting primarily of securities shall be deemed a consolidation or merger for the foregoing purposes.

(f) No adjustment in the Per Share Warrant Price shall be required unless such adjustment would require an increase or decrease of at least $0.05 per share of Common Stock; provided, however, that any adjustments which by reason of this Subsection 3(f) are not required to be made shall be carried forward and taken into account in any subsequent adjustment; provided, further, however, that adjustments shall be required and made in accordance with the provisions of this Section 3 (other than this Subsection 3(f)) not later than such time as may be required in order to preserve the tax-free nature of a distribution to the Holder of this Warrant or Common Stock issuable upon the exercise hereof. All calculations

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under this Section 3 shall be made to the nearest cent or to the nearest 1/100th of a share, as the case may be. Anything in this Section 3 to the contrary notwithstanding, the Company shall be entitled to make such reductions in the Per Share Warrant Price, in addition to those required by this Section 3, as it in its discretion shall deem to be advisable in order that any stock dividend, subdivision of shares or distribution of rights to purchase stock or securities convertible or exchangeable for stock hereafter made by the Company to its stockholders shall not be taxable.

(g) Whenever the Per Share Warrant Price is adjusted as provided in this Section 3 and upon any modification of the rights of a Holder of Warrants in accordance with this Section 3, the Company shall promptly prepare a brief statement of the facts requiring such adjustment or modification and the manner of computing the same and cause copies of such certificate to be mailed to the Holders of the Warrants.

(h) If the Board of Directors of the Company shall declare any dividend or other distribution with respect to the Common Stock other than a cash distribution out of earned surplus, the Company shall mail notice thereof to the Holders of the Warrants not less than ten (10) days prior to the record date fixed for determining stockholders entitled to participate in such dividend or other distribution.

(i) If, as a result of an adjustment made pursuant to this Section 3, the Holder of any Warrant thereafter surrendered for exercise shall become entitled to receive shares of two or more classes of capital stock or shares of Common Stock and other capital stock of the Company, the Board of Directors (whose determination shall be conclusive and shall be described in a written notice to the Holder of any Warrant promptly after such adjustment) shall determine the allocation of the adjusted Per Share Warrant Price between or among shares or such classes of capital stock or shares of Common Stock and other capital stock.

(j) Upon the expiration of any rights, options, warrants or conversion privileges with respect to the issuance of which an adjustment to the Per Share Warrant Price had been made, if such option, right, warrant or conversion shall not have been exercised, the number of Warrant Shares purchasable upon exercise of this Warrant, to the extent this Warrant has not then been exercised, shall, upon such expiration, be readjusted and shall thereafter be such as they would have been had they been originally adjusted (or had the original adjustment not been required, as the case may be); provided, however, that no such readjustment shall have the effect of decreasing the number of Warrant Shares purchasable upon exercise of this Warrant by an amount in excess of the amount of the adjustment initially made in respect of the issuance, sale or grant of such rights, options, warrants or conversion privileges.

(k) In case any event shall occur as to which the other provisions of this Section 3 are not strictly applicable but as to which the failure to make any adjustment would not fairly protect the purchase rights represented by this Warrant in accordance with the essential intent and principles hereof then, in each such case, the Board of Directors of the Company shall in good faith determine the adjustment, if any, on a basis consistent with the essential intent and principles established herein, necessary to preserve the purchase rights represented by the Warrants. Upon such determination, the Company will promptly mail a copy thereof to the Holder of this Warrant and shall make the adjustments described therein.

4. Fully Paid Stock; Taxes. The shares of the Common Stock represented by each and every certificate for Warrant Shares delivered on the exercise of this Warrant shall at the time of such delivery, be duly authorized, validly issued and outstanding, fully paid and nonassessable, and not subject to preemptive rights or rights of first refusal, and the Company will take all such actions as may be necessary to assure that the par value, if any, per share of the Common Stock is at all times equal to or less than the then Per Share Warrant Price. The

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Company shall pay, when due and payable, any and all Federal and state stamp, original issue or similar taxes which may be payable in respect of the issue of any Warrant Share or any certificate thereof to the extent required because of the issuance by the Company of such security.

5. Registration Under Securities Act of 1933.

(a) The Holder shall have the right to participate in the registration rights granted to purchasers of the Common Stock pursuant to Article V of the subscription agreement (the “Subscription Agreement”) between such purchasers and the Company that were entered into at the time of the initial sale of the Common Stock. By acceptance of this Warrant, the Holder agrees to comply with the provisions in Article V of the Subscription Agreement to same extent as if it were a party thereto.

(b) Until all of the Warrant Shares have been sold under a Registration Statement or pursuant to Rule 144(k), so long as the Company’s Common Stock remains registered under the Securities Act of 1934, as amended, the Company shall use its reasonable best efforts to file with the Securities and Exchange Commission all current reports and the information as may be necessary to enable the Holder to effect sales of its shares in reliance upon Rule 144(k) promulgated under the Act.

6. Investment Intent; Limited Transferability.

(a) By accepting this Warrant the Holder represents , that it understands that this Warrant and any securities obtainable upon exercise of this Warrant have not been registered for sale under Federal or state securities laws and are being offered and sold to the Holder pursuant to one or more exemptions from the registration requirements of such securities laws. In the absence of an effective registration of such securities or an exemption therefrom, any certificates for such securities shall bear the legend set forth on the first page hereof. The Holder understands that it must bear the economic risk of its investment in this Warrant and any securities obtainable upon exercise of this Warrant for an indefinite period of time, as this Warrant and such securities have not been registered under Federal or state securities laws and therefore cannot be sold unless subsequently registered under such laws, unless an exemption from such registration is available.

(b) The Holder, by its acceptance of this Warrant, represents to the Company that it is acquiring this Warrant and will acquire any securities obtainable upon exercise of this Warrant for its own account for investment and not with a view to, or for sale in connection with, any distribution thereof in violation of the Securities Act of 1933, as amended (the “Act”). The Holder agrees that this Warrant and any such securities will not be sold or otherwise transferred unless (i) a registration statement with respect to such transfer is effective under the Act and any applicable state securities laws or (ii) such sale or transfer is made pursuant to one or more exemptions from the Act as supported by an opinion of counsel to the Holder.

(c) This Warrant may not be sold, transferred, assigned or hypothecated for six (6) months from the date hereof except (i) to any firm or corporation that succeeds to all or substantially all of the business of Paramount Capital, Inc., (ii) to any of the officers, employees, associates or affiliated companies of Paramount Capital, Inc., or of any such successor firm, (iii) to any NASD member participating in the Offering or any officer or employee of any such NASD member or (iv) in the case of an individual, pursuant to such individual’s last will and testament or the laws of descent and distribution, and is so transferable only upon the books of the Company which the Company shall cause to be maintained for such purpose. The Company may treat the registered Holder of this Warrant as it appears on the Company’s books at any time

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as the Holder for all purposes. The Company shall permit any Holder of a Warrant or its duly authorized attorney, upon written request during ordinary business hours, to inspect and copy or make extracts from its books showing the registered Holders of Warrant. All Warrants issued upon the transfer or assignment of this Warrant will be dated the same date as this Warrant, and all rights of the holder thereof shall be identical to those of the Holder.

7. Loss, etc., of Warrant. Upon receipt of evidence satisfactory to the Company of the loss, theft, destruction or mutilation of this Warrant, and of indemnity reasonably satisfactory to the Company, if lost, stolen or destroyed, and upon surrender and cancellation of this Warrant, if mutilated, the Company shall execute and deliver to the Holder a new Warrant of like date, tenor and denomination.

8. Warrant Holder Not Stockholder. This Warrant does not confer upon the Holder any right to vote on or consent to or receive notice as a stockholder of the Company, as such, in respect of any matters whatsoever, nor any other rights or liabilities as a stockholder, prior to the exercise hereof; this Warrant does, however, require certain notices to Holders as set forth herein.

9. Communication. No notice or other communication under this Warrant shall be effective unless, however, any notice or other communication shall be effective and shall be deemed to have been given if, the same is in writing and is mailed by first-class mail, postage prepaid, addressed to:

(a) the Company at Point Therapeutics, Inc., 125 Summer St., Boston, MA 02110 Facsimile: (617) 933-2130, Attn: President, or such other address as the Company has designated in writing to the Holder, or

(b) the Holder at c/o Paramount Capital, Inc., 787 Seventh Avenue, 48^th Floor, New York, NY 10019 or other such address as the Holder has designated in writing to the Company.

10. Headings. The headings of this Warrant have been inserted as a matter of convenience and shall not affect the construction hereof.

11. Applicable Law. This Warrant shall be governed by and construed in accordance with the law of the State of New York without giving effect to the principles of conflicts of law thereof.

12. Amendment, Waiver, etc. Except as expressly provided herein, neither this Warrant nor any term hereof may be amended, waived, discharged or terminated other than by a written instrument signed by the party against whom enforcement of any such amendment, waiver, discharge or termination is sought; provided, however, that any provisions hereof may be amended, waived, discharged or terminated upon the written consent of the Company and the Majority of the Holders.

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IN WITNESS WHEREOF, the Company has caused this Warrant to be signed by its President and has caused its corporate seal to be hereunto affixed and attested by its Secretary this      day of September, 2003.

ATTEST:

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SUBSCRIPTION (cash)

The undersigned,                    , pursuant to the provisions of the foregoing Warrant, hereby agrees to subscribe for and                      purchase shares of the Common Stock, par value $.01 per share, of Point Therapeutics, Inc. covered by said Warrant, and makes payment therefor in full at the price per share provided by said Warrant.

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CASHLESS EXERCISE

The undersigned                     , pursuant to the provisions of the foregoing Warrant, hereby elects to exchange its Warrant for                      shares of Common Stock, par value $.01 per share, of Point Therapeutics, Inc. pursuant to the Cashless Exercise provisions of the Warrant.

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ASSIGNMENT

FOR VALUE RECEIVED                      hereby sells, assigns and transfers unto                      the foregoing Warrant and all rights evidenced thereby, and does irrevocably constitute and appoint                     , attorney, to transfer said Warrant on the books of Point Therapeutics, Inc.

PARTIAL ASSIGNMENT

FOR VALUE RECEIVED                      hereby assigns and transfers unto                      the right to purchase                      shares of Common Stock, par value $.01 per share, of Point Therapeutics, Inc. covered by the foregoing Warrant, and a proportionate part of said Warrant and the rights evidenced thereby, and does irrevocably constitute and appoint                     , attorney, to transfer such part of said Warrant on the books of Point Therapeutics, Inc.

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