<PAGE>

                                                                 Exhibit No. 4.1

                              AMENDING AGREEMENT

          This Amendment Agreement (this "Amendment"), dated as of January 3,
                                          ---------
2002, is entered into by and among Constellation 3D Technology Limited, a
corporation organized under the laws of the British Virgin Islands ("ConTech"),
                                                                     -------
TIC Target Invest Consulting, LLC, a financing corporation organized under the
laws of St. Kitts & Nevis ("TIC") with its principal office located at Churer
                            ---
Strasse 35, CH-9470, Buchs, SG, Switzerland and Constellation 3D, Inc., a
Delaware corporation ("C3D").
                       ---

          A.  TIC and ConTech are parties to that certain Loan Agreement, dated
as of November 17, 2001 (the "Loan Agreement").
                              --------------

          B.  ConTech and C3D are parties to that certain Option Agreement,
dated as of November 17, 2001 (the "Option Agreement").
                                    ----------------

          C.  For good and valuable consideration, the receipt and sufficiency
of which is hereby acknowledged, the parties hereto agree as follows:

          1.  Amendments to Loan Agreement.
              ----------------------------

          (a) Each of TIC and ConTech hereby agree that the first sentence in
Section 2.4(a) of the Loan Agreement is hereby amended in its entirety to read
as follows:

          "Within fifty-one (51) Business Days after the Closing Date, the
          Lender shall designate a date which is a Business Day within sixty-two
          (62) Business Days after the Closing Date for the funding of the Loan
          (the "Funding Date")."
                ------------

          (b) Each of TIC and ConTech hereby agree that the references to
"Schedule 3.5" and "Schedule 3.11" in Section 3.4 and Section 3.9, respectively,
 ------------       -------------
of the Loan Agreement are hereby amended to be references to "Schedule 3.4" and
                                                              ------------
"Schedule 3.9," respectively.
 ------------

          2.  Agreement Relating to Bridge Note.
              ---------------------------------

          (a) Each of C3D and ConTech agree that:

              (i)  Upon and subject to ConTech's receipt of $2,000,000 pursuant
                   to a Bridge Note between ConTech and TIC (the "TIC Bridge
                   Note"), ConTech shall advance the $2,000,000 to C3D pursuant
                   to the terms of a Bridge Note between C3D and ConTech, a form
                   of which is attached hereto as Attachment A (the "Bridge
                   Note"); and

              (ii) Simultaneous with the funding of the Bridge Note, C3D shall
                   execute and deliver the Bridge Note to ConTech.

          (b) Each of ConTech and TIC agree that:
<PAGE>

               (i)  TIC shall, by January 31, 2002, advance $2,000,000 to
                    ConTech pursuant to the terms of the TIC Bridge Note, a form
                    of which is attached hereto as Attachment B; and

               (ii) Simultaneous with the funding of the TIC Bridge Note,
                    ConTech shall execute and deliver the TIC Bridge Note to
                    TIC.

          3.   Additional Agreement regarding the Loan Agreement.  Each of TIC
               -------------------------------------------------
and ConTech hereby acknowledges and agrees that Schedule 3.3, Schedule 3.4 and
                                                ------------  ------------
Schedule 3.9 of the Loan Agreement contain no disclosures.
------------

          4.   Amendment to Option Agreement. Each of ConTech and C3D hereby
               -----------------------------
agree that the provisions of Section 4(b), Section 4(c), Section 4(d), Section
4(e) and Section 4(f) of the Option Agreement are each hereby deleted in their
entirety and in each case replaced with the word "Reserved".

          5.   Miscellaneous. Except as modified by this Amendment, the terms of
               -------------
the Loan Agreement and the Option Agreement, respectively, shall remain in full
force and effect. This Amendment may be executed by any of the parties to this
Amendment on separate counterparts and all of said counterparts taken together
shall be deemed to constitute one and the same instrument.

                           [signature page follows]
<PAGE>

          IN WITNESS WHEREOF, the parties hereto have caused this Amendment to
be executed and delivered by their duly authorized officers as of the date first
written above.

                         CONSTELLATION 3D TECHNOLOGY LIMITED

                         By:  /s/  Eugene Levich
                            --------------------------------
                            Name:  Eugene Levich
                            Title: Director

                         CONSTELLATION 3D, INC.

                         By:  /s/ Michael Goldberg
                            --------------------------------
                            Name: Michael Goldberg
                            Title: Secretary and Director of Legal Affairs

                         TIC TARGET INVEST CONSULTING, LLC

                         By: /s/ Andre Khayyam
                            --------------------------------
                            Name:  Andre Khayyam
                            Title: Managing Director


ACKNOWLEDGMENT

          The undersigned hereby acknowledges that the term "Funding Date," as
used in the Loan Agreement, dated as of November 17, 2001, by and between
ConTech and the undersigned shall have the meaning ascribed to such term in
Section 2.4(a) of the Loan Agreement, as amended pursuant to the terms of this
Amendment.

                         CONSTELLATION 3D, INC.

                         By:  /s/ Michael Goldberg
                             ----------------------------
                            Name: Michael Goldberg
                            Title: Secretary and Director of Legal Affairs