TRADEMARK SECURITY AGREEMENT

Exhibit 10.3

TRADEMARK SECURITY AGREEMENT

TRADEMARK SECURITY AGREEMENT, dated as of August 12, 2005, by CARDIMA, INC. (referred to as “Grantor”), in favor of APIX INTERNATIONAL LIMITED (the “Secured Party”) is made with reference to the following:

WITNESSETH:

WHEREAS, pursuant to that certain Term Sheet (“Term Sheet”) dated as of August 12, 2005 and that certain Promissory Note (the “Bridge Promissory Note”) dated as of August 12, 2005 between Grantor and the Secured Party, each of which the parties hereto propose to cause to be superseded by a Loan Agreement (the “Loan Agreement”) and Promissory Note (the “Promissory Note”) by and between Grantor and the Secured Party (the Bridge Promissory Note, the Term Sheet, the Loan Agreement and the Promissory Note, including all annexes, exhibits or schedules thereto, as from time to time amended, restated, supplemented or otherwise modified, collectively, the “Funding Documents”), the Lender has agreed to make certain loans to Borrower subject to and in accordance with the terms and conditions of the Funding Documents;

WHEREAS, the Secured Party is willing to make certain loans as provided for in the Funding Documents, but only upon the condition, among others, that Grantor shall have executed and delivered to the Secured Party that certain Patent, Trademark and Copyright Security Agreement dated as of the date hereof (including all annexes, exhibits or schedules thereto, as from time to time amended, restated, supplemented or otherwise modified, collectively referred to as the “IP Security Agreement”);

WHEREAS, pursuant to the IP Security Agreement, Grantor is required to execute and deliver this Trademark Security Agreement to the Secured Party,

NOW, THEREFORE, in consideration of the premises and mutual covenants herein contained and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, Grantor hereby agrees as follows:

1. DEFINED TERMS. All capitalized terms used but not otherwise defined herein shall have the meanings given to them in the IP Security Agreement.

2. GRANT OF SECURITY INTEREST IN TRADEMARK COLLATERAL. Grantor hereby grants to the Secured Party a continuing first priority security interest in all of Grantor’s right, title and interest in, to and under the following, whether presently existing or hereafter created or acquired (collectively, the “Trademark Collateral”):

(a) all of the trademarks referred to on Schedule I hereto and all registrations thereof;

(b) all applications for registration of any such Trademarks now or hereafter filed by Grantor, including those referred to on Schedule I hereto;

(c) all goodwill of the business connected with the use of, and symbolized by, each such Trademark and Trademark License; and

(d) all products and proceeds of the foregoing, including, without limitation, any claim by Grantor against third parties for past, present or future (i) infringement or dilution of any Trademark or any Trademark licensed under any Trademark License or (ii) injury to the goodwill associated with any Trademark or any Trademark licensed under any Trademark License.

3. SECURITY AGREEMENT. The security interests granted pursuant to this Trademark Security Agreement are granted in conjunction with the security interests granted to the Secured Party pursuant to the IP Security Agreement. Grantor hereby acknowledges and affirms that the rights and remedies of the Secured Party with respect to the continuing first priority security interest in the Trademark Collateral made and granted hereby are more fully set forth in the IP Security Agreement, the terms and provisions of which are incorporated by reference herein as if fully set forth herein.

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IN WITNESS WHEREOF, Grantor has caused this Trademark Security Agreement to be executed and delivered by its duly authorized officer as of the date first set forth above.

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ACKNOWLEDGMENT OF GRANTOR

STATE OF                     )

                                         )ss.

COUNTY OF                 )

On this day of      August, 2005 before me personally appeared                             , proved to me on the basis of satisfactory evidence to be the person who executed the foregoing instrument on behalf of Cardima, Inc., who being by me duly sworn did depose and say that such Person is an authorized officer of said corporation, that the said instrument was signed on behalf of said corporation authorized by its Board of Directors and that such Person acknowledged said instrument to, be the free act and deed of said corporation.

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SCHEDULE I

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TRADEMARK SECURITY AGREEMENT

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