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                                                                     Exhibit 3.4
                                                                      0098012007

                               TRADEMARK AGREEMENT

THIS AGREEMENT dated December 11, 1998 ("Effective Date") by and between ING. C.
OLIVETTI & C., S.p.A., an Italian company with registered office at Via Jervis
77, 10015 Ivrea, Italy (hereinafter called "Olivetti") and OLICOM A/S, a Danish
company with offices at Nybrovej 114, DK-2800 Lyngby, Denmark (hereinafter
called "Company"), acting on its behalf and on behalf of its Subsidiaries, as
defined below,

                                   WITNESSETH:

WHEREAS, Olivetti is the owner of the trademark "OLICOM" and the related
registrations set forth in Schedule A to this Agreement (such trademark and
registrations, including any other registration that Olivetti may apply for
and/or obtain in any country being hereinafter called "the Trademark");

WHEREAS, Company is licensed by Olivetti to use the Trademark in Denmark and
elsewhere in accordance with the terms of the Trademark Agreement dated
September 2, 1992, as amended on June 10, 1993 (hereinafter called the "Existing
Agreement'); and

WHEREAS, the parties wish to restructure the terms and conditions of the
existing Trademark Agreement as set forth herein;

NOW, THEREFORE, it is agreed as follows:

SECTION 1 - GRANT OF LICENSE

a) Olivetti hereby grants a worldwide, exclusive license to Company and its
Subsidiaries, subject to the terms and conditions of this Agreement, to use the
Trademark on or in connection with the sourcing, imparting, exporting,
manufacture, promotion, advertising, merchandising, sale and offering for sale
and distribution of Company's products and services, including products and
services procured on OEM basis, and as corporate or business name of Company and
its Subsidiaries,

b) The term "Subsidiaries" of either party, as used herein, shall mean any
corporation or other business organization in which such party owns the majority
of the shares entitled to vote in the Shareholders' ordinary meetings, For
avoidance of doubt, Olicom, Inc., a Texas corporation, is a Subsidiary of
Company.

c) Company acknowledges the trademark co-existence agreement entered into by
Olivetti on April 8, 1992 with Olympus optical Co, (Europa) GmbH, a copy of
which has been delivered to Company prior to the execution of this Agreement,
and therefore Company agrees that neither it nor its Subsidiaries shall use the
Trademark on or in connection with the following products: dictating machines
(including tape cassettes therefor), photocopying machines, facsimile equipment,
electronic person identification apparatus, and telephone equipment.
Additionally, 

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Company agrees that neither it nor its Subsidiaries shall use the Trademark in
connection with telecommunication services of the type provided by Olivetti or
its Subsidiaries.

d) For the term of this Agreement and for one year thereafter, Olivetti shall
not use itself, nor grant to any third party (including Olivetti's Subsidiaries)
any right to use the Trademark on or in connection with products or services of
the type manufactured or marketed, or offered by Company and its Subsidiaries.
During the term of this Agreement, Olivetti shall not use itself, nor grant to
any third party (including Olivetti's Subsidiaries) any right to use the
Trademark on or in connection with any product or service or as corporate name
or business name.

SECTION 2 - QUALITY STANDARDS

a) Company and its Subsidiaries undertake to use the Trademark only on or in
connection with products or services which meet the reasonable quality standards
established by Olivetti and notified to Company from time to time. Olivetti
agrees that the products and services presently offered by the Company satisfy
the requirements of this Section 2.

b) Upon Olivetti's request, Company shall provide samples of its and its
Subsidiaries' products to Olivetti to permit Olivetti to inspect their quality
level and conformance to this Agreement. Such products shall be considered
approved if written notice of disapproval is not received by the Company within
thirty (30) days after their being provided to Olivetti, Once approval has been
obtained, further approvals need not be obtained for additional or repeated use
of the same or substantially similar materials. Olivetti agrees that the
materials presently being used by the Company are approved. Company and its
Subsidiaries shall not use the Trademark on or in connection with any product
which has been rejected by Olivetti by written notice to Company upon such
inspection.

SECTION 3 - APPEARANCE OF TRADEMARK

a) Company and its Subsidiaries agree to strictly comply with the rules
established by Olivetti and notified by Company from time to time with respect
to the appearance and manner of presentation of Olivetti's trademarks.
Representative samples of products, literature or other items where the
Trademark is used shall be provided by Company to Olivetti at the latter's
request. Such literature or other items shall be considered approved if notice
of disapproval is not received by the Company within ten (10) days.

b) If so required by Olivetti in writing, Company shall indicate in the manner
specified by Olivetti that the Trademark is owned by Olivetti,

SECTION 4 - REGISTRATION, ENFORCEMENT AND DEFENSE OF THE TRADEMARK

a) Company and its Subsidiaries shall not register in any country, directly or
indirectly, the Trademark or any other name suggesting a connection with
Olivetti, subject to Section 8(c) hereof. At Company's request and expense,
Olivetti shall apply to register the Trademark, where possible, and Olivetti
shall identify Company as its registered user under the Trademark. If so
requested by Company, such applications in the name of Olivetti shall be done
through patent firms retained by Company, in proper coordination with Olivetti,


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b) Prosecution of any infringer of the Trademark shall be at Olivetti's sole
judgment and under its sole control. If Olivetti declines to do so, Company may
take action to stop such infringement provided such action does not impair
Olivetti's rights in the Trademark,

c) In the event any third party should make or file any claim for trademark
infringement against Company arising out of the use of the Trademark, Company
shall promptly notify Olivetti which will undertake at Company's expense
reasonable efforts to have such claim withdrawn, settled or defended. Company
shall cooperate with and assist such efforts by Olivetti.

SECTION 5 - LICENSE FEES

In consideration of the rights granted by Olivetti to Company and its
Subsidiaries under this Agreement, Company shall pay to Olivetti the following
fees:

a) An upfront fee of One Hundred and Fifty Thousand US Dollars (US$ 150,000,000)
payable on January 30, 1999;

b) For each twelve month period starting with September 2, 1999 during the term
of this Agreement, a yearly fee of One Hundred Thousand US Dollars (US$
100,000), payable in quarterly installments of US$ 25,000 at the end of each
calendar quarter.

c) Each payment set forth above shall be made in US currency by wire transfer to
Olivetti's account number No. 1023 of "Istituto Bancario S. Paolo di Torino",
Ivrea branch (ABI 1025, CAB 30540), unless otherwise indicated in writing by
Olivetti.

d) Company may withhold taxes from the fees set forth above up only to the
extent that (1) such withholding is compulsory under the Danish laws, (ii)
Company has availed itself of the applicable tax treaty, the tax withholding
does not exceed five percent (5%) and (iv) Company provides to Olivetti a
receipt of the tax paid, suitable to claim tax credit in Italy. In the event
that the tax withholding exceeds 5%, the fees shall be increased to result into
net payments to Olivetti equal to the fees less 5%. Olivetti will provide to the
Company all documents required under the applicable tax treaty, as specified in
writing by Company.

e) Delayed payments shall bear interest at the rate of five percentage points
over the offered interbank rate for six months deposits in US Dollars as
published by "Sole - 24 Ore" or, absent such publication, as otherwise announced
by Associazione Bancaria Italiana.

SECTION 6 - ASSIGNMENT AND CHANGE OF CONTROL

a) Without Olivetti's prior consent, which shall not be unreasonably withheld,
the license and any rights herein granted shall not be assigned or otherwise
transferred by Company or its Subsidiaries and shall not inure to the benefit of
any other person, including a successor of the Company or a trustee in
bankruptcy.

b) Olivetti may terminate this Agreement by ninety (90) days written notice to
Company stating a reasonable ground for such termination, in the event that the
majority of the voting shares in the Company are acquired by a third party,
where such third party is a direct competitor 


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of Olivetti or its Subsidiaries, provided that Olivetti shall not unreasonably
exercise this termination right,

SECTION 7 - TERM OF AGREEMENT

a) This Agreement and the license granted herein shall become effective on the
Effective Date, and shall continue in effect for the term of this Agreement as
specified in the following paragraph b) unless earlier terminated as provided in
Section 8 hereof.

b) Subject to Section 8, the term of this Agreement shall be until September 1,
2009, provided that Company shall have the right, by giving Olivetti's written
notice at least six months prior to such date, to renew this Agreement for
further tan (10) years under the same terms and conditions, except that fees
shall be adjusted in light of inflation to reflect the variation in the Consumer
Price Index for All Urban Consumers (CPI-U), as calculated by the US Bureau of
Labor Statistics, from the Effective Date to September 2, 2009. In the event
that the CPI-U is discontinued, the closest index shall be determined by mutual
agreement.

SECTION 8 - TERMINATION

a) Company shall have the right to terminate this Agreement for convenience by
giving Olivetti at least twelve (12) months written notice prior to the
beginning of a yearly period starting with September 2"' of any year,

b) In addition to the termination right pursuant to Section 6(b), Olivetti shall
have the right to terminate this Agreement by written notice to Company in any
of the following events, and in any such event the termination shall be
immediately effective upon Olivetti's giving of such notice, without the need
for any judicial action and without prejudice to any other relief to which
Olivetti may be entitled:

                  (i) if Company or any of its Subsidiaries are in default of
         this Agreement and fail to cure such default within thirty (30) days
         after the date of Olivetti's notification of the default to Company; or

                  (ii) if Company or its Subsidiaries file a petition in
         bankruptcy or are adjudicated bankrupt or make a general assignment in
         favor of creditors or become insolvent, or in the event that any
         procedure for the liquidation or dissolution of Company or its
         Subsidiaries is initiated.

c) Upon expiration or termination of this Agreement all licenses granted herein
shall terminate, and Company and its Subsidiaries shall immediately start, and
complete within a reasonable period not exceeding twelve (12) months, actions to
cease using the Trademark in any manner, including change of their corporate
name to a new one that does not contain the Trademark or otherwise suggests a
connection with Olivetti. The parties agree that a name like "Colicom" would not
be deemed as indicating a connection with Olivetti. For a period of twelve (12)
months following Olivetti's notice of termination under this Section or Section
6(b), Company and its Subsidiaries shall be permitted to sell or otherwise
distribute (in a manner consistent with the reputation of the Trademark) (i) its
inventory of products bearing the 


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Trademark which exists on the date of such notice, and (H) all items ordered
prior to such notice, if the related purchase order cannot be canceled.

d) Company shall be entitled to associate the Trademark to another tradename
owned by it, so as to achieve a smooth transition upon termination of this
Agreement.

SECTION 9 - MISCELLANEOUS PROVISIONS

a) Company hereby acknowledges Olivetti's rights to the Trademark, and that the
license granted hereunder is conditional upon fulfillment of the obligations
contained herein, including without limitation the obligation on termination to
cease using the Trademark as part of the corporate name of Licensee or its
Subsidiaries.

b) This Agreement shall be governed by the Italian law.

c) The Existing Agreement is hereby superseded.

ING. C. OLIVETTI & C., S.p.A.                 OLICOM A/S

by:      /s/  Roberto Colaninno               by:      /s/  Niels Christian Furu

name:    Roberto Colaninno                    name:    Niels Christian Furu

title:   CEO                                  title:   President, CEO

date:    December 15, 1998                    date:    December 11, 1998


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                                    EXHIBIT A

                  List of Registrations of the Trademark OLICOM

DENMARK

Registration Number 1048-1988, classes 9, 16, 38 and 42, registered on March 11,
1988. 1



ITALY 

Registration Number 411098, class 9, registered on March 10, 1986.



USA 

Registration Number 1,867,494, class 9, registered on December 13, 1994.