POINT THERAPEUTICS, INC.

Exhibit 1.3

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 [            ], its designee or its permitted assigns is entitled to purchase from the Company, at any time or from time to time commencing on                   ,2003 and prior to 5:00 P.M., New York City time, on                  , 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 (subject to adjustment) 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”; and (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 Warrants Shares are referred to as the “Majority of the Holders”). The Aggregate Warrant Price is not subject to adjustment.

This Warrant, together with warrants of like tenor, constituting in the aggregate Warrants to purchase [            ] Warrant Shares, was originally issued pursuant to an Subscription Agreement (the “Subscription Agreement”) between the Company and the investor named therein in connection with a private placement by the Company of its securities. By acceptance of this Warrant, the Holder agrees to comply with all applicable provisions of the Subscription Agreement

1. Exercise of Warrant.

(a) This Warrant may be exercised in whole at any time, or in part from time to time, commencing on                  , 2003 and prior to 5:00 P.M., New York City time, on                   , 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

(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 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

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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) 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(c) 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.

(d) 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 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.

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(e) 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.

(f) 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.

(g) 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.

(h) 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 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

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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) In addition to the limitations set forth in Section 1, this Warrant may not be sold, transferred, assigned or hypothecated by the Holder except in compliance with the provisions of the Act and the applicable state securities “blue sky” laws, and is so transferable only upon the books of the Company which it 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 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. Optional Redemption. In the event that the closing price of the Common Stock for any 10 consecutive Trading Days is at least $8.00 (the “Redemption Price”), the Company shall be entitled to redeem the Warrants, or any of them, at a per Warrant redemption price of $0.001, by 30 business days’ written notice to the Holder. A “Trading Day” shall mean any day on which shares of the Company’s Common Stock are sold on the respective exchange. Upon the expiration of such 30 business day period, all Warrants noticed for redemption that have not theretofore been exercised by the Holder shall, upon payment of the aggregate redemption price therefore, cease to represent the right to purchase any shares of Common Stock and shall be deemed cancelled without any further act or deed on the part of the Company. The Holder agrees to return the certificate representing any redeemed Warrants to the Company upon their redemption and to indemnify the Company with respect to any losses, claims, damages or liabilities arising from the Holder’s failure to return such certificate. In the event the certificate so returned represents a number of Warrants in excess of the number being redeemed, the Company shall as promptly as practicable issue to the Holder a new certificate for the number of unredeemed Warrants.

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8. 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.

9. 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.

10. 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              or other such address as the Holder has designated in writing to the Company.

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

12. 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.

13. 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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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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