<PAGE>

                                                                   Exhibit 10.15

                       THIRD LOAN MODIFICATION AGREEMENT


     This Third Loan Modification Agreement is entered into as of December 22,
2000, by and between CENTRA SOFTWARE, INC., a Delaware corporation with its
principal place of business at 430 Bedford Street, Lexington, Massachusetts
02173 ("Borrower") and SILICON VALLEY BANK, a California-chartered bank
("Bank"), with its principal place of business at 3003 Tasman Drive, Santa
Clara, CA 95054 and with a loan production office located at Wellesley Office
Park, 40 William Street, Suite 350, Wellesley, MA 02481, doing business under
the name "Silicon Valley East".

1.   DESCRIPTION OF EXISTING INDEBTEDNESS. Among other indebtedness which may be
     ------------------------------------
owing by Borrower to Bank, Borrower is indebted to Bank pursuant to a loan
arrangement dated as of November 5, 1997, evidenced by, among other documents, a
certain Loan and Security Agreement dated as of November 5, 1997, as affected
and amended by (i) a First Loan Modification Agreement dated December 30, 1998,
and (ii) a Second Loan Modification Agreement dated April 12, 1999 (the "Loan
Agreement").  The Loan Agreement established: (i) a working capital line of
credit in favor of the Borrower in the maximum principal amounts of Seven
Hundred Fifty Thousand Dollars ($750,000.00) (the "Committed Revolving Line"),
(ii) two equipment lines of credit in favor of the Borrower in the maximum
principal amount of Five Hundred Thousand Dollars ($500,000.00) and Six Hundred
Thousand Dollars ($600,000.00), respectively (collectively, the "Equipment
Lines"), and (iii) a bridge line in favor of the Borrower in the amount of One
Million Five Hundred Thousand Dollars ($1,500,000.00).  Capitalized terms used
but not otherwise defined herein shall have the same meaning as in the Loan
Agreement.

Hereinafter, all indebtedness, liabilities, and other Obligations owing by
Borrower to Bank shall be referred to as the "Indebtedness".

2.   DESCRIPTION OF COLLATERAL AND GUARANTIES.  Repayment of the Indebtedness is
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secured by the Collateral as described in the Loan Agreement (together with any
other collateral security granted to Bank, the "Security Documents").

Hereinafter, the Security Documents, together with all other documents
evidencing or securing the Indebtedness shall be referred to as the "Existing
Loan Documents".

3.   DESCRIPTION OF CHANGE IN TERMS.
     ------------------------------

     A.   Modification(s) to Loan Agreement.

          1.   The Loan Agreement shall be amended by deleting the following
               definition appearing in Section 1.1 thereof:

                    ""Equipment Advance" or "Equipment Advances" shall mean any
                    advance made hereunder pursuant to Section 2.1.2 or Section
                    2.1.3."

               and inserting in lieu thereof the following:

                    ""Equipment Advance" or "Equipment Advances" shall mean any
                    advance made hereunder pursuant to Section 2.1.2 , Section
                    2.1.3, or Section 2.1.5."

          2.   The Loan Agreement shall be amended by deleting the following
               definition appearing in Section 1.1 thereof:
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                    ""Maturity Date" means the later of (w) the Equipment
                    Maturity Date, (x) the 1999 Equipment Maturity Date, (y) the
                    Revolving Maturity Date, or (z) the Bridge Maturity Date."

               and inserting in lieu thereof the following:

                    ""Maturity Date" means the later of (w) the Equipment
                    Maturity Date, (x) the 1999 Equipment Maturity Date, (y) the
                    2000 Equipment Maturity Date, or (z) the Revolving Maturity
                    Date"

          3.   The Loan Agreement shall be amended by inserting the following
               definitions immediately after the definition of "Total
               Liabilities" appearing in Section 1.1 thereof:

                    ""Unused Line Fee" has the meaning set forth in Section
                    2.1.5(e).

                    "2000 Committed Equipment Line" means a Credit Extension of
                    up to Two Million Dollars ($2,000,000.00)."

                    "2000 Equipment Availability End Date" has the meaning set
                    forth in Section 2.1.5.

                    "2000 Equipment Maturity Date" means September 22, 2004."

          4.   The Loan Agreement shall be amended by inserting after Section
               2.1.4 thereof the following new Section 2.1.5 entitled "2000
               Equipment Advances":

                    "2.1.5    2000 Equipment Advances.
                              -----------------------

                    (a)  Subject to and upon the terms and conditions of this
                    Agreement, at any time through September 22, 2001 (the "2000
                    Equipment Availability End Date"), Bank agrees to make
                    Equipment Advances (each an "Equipment Advance" and
                    collectively, the "Equipment Advances") to Borrower under
                    this Section 2.1.5 in an aggregate outstanding amount not to
                    exceed the 2000 Committed Equipment Line.  To evidence the
                    Equipment Advances, Borrower shall deliver to Bank, at the
                    time of each Equipment Advance request, an invoice for the
                    equipment to be purchased. Each invoice submitted at the
                    time of each Equipment Advance request may not be more than
                    ninety (90) days past the invoice date in order to be
                    eligible for an Equipment Advance; provided, however, that
                    in connection with the initial Equipment Advance only
                    invoices submitted to Bank for financing under the 2000
                    Committed Equipment Line  may have invoice dates from and
                    after January 1, 2000.  The Equipment Advances shall be used
                    only to purchase Equipment and shall not exceed One Hundred
                    Percent (100%) of the invoice amount of such equipment
                    approved from time to time by Bank, excluding taxes,
                    shipping, warranty charges, freight discounts and
                    installation expense.  Software may only constitute up to
                    $250,000.00 of aggregate Equipment Advances made under the
                    2000 Committed Equipment Line.

                    (b)  Interest shall accrue from the date of each Equipment
                    Advance under the 2000 Committed Equipment Line made
                    pursuant to this Section 2.1.5 at a per annum rate equal to
                    the aggregate of the Prime Rate, plus one half of one
                                                     ----
                    percent (0.50%).  Interest on each Equipment Advance under
                    the 2000

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<PAGE>

                    Committed Equipment Line shall be payable monthly on the
                    Payment Date of each month through the month in which the
                    2000 Equipment Availability End Date falls. Amounts
                    currently amortizing under Sections 2.1.2 and 2.1.3 above
                    shall continue to be repaid as provided respectively in
                    Sections 2.1.2 and 2.1.3 above, and shall be treated as
                    existing Equipment Advances under the 1997 Committed
                    Equipment Line and 1999 Committed Equipment Line,
                    respectively. Any Equipment Advances made pursuant to this
                    Section 2.1.5 that are outstanding on the 2000 Equipment
                    Availability End Date will be payable in thirty-six (36)
                    equal monthly installments of principal, plus all accrued
                    interest, beginning on the Payment Date of the month
                    following the 2000 Equipment Availability End Date and
                    continuing on the Payment Date of each month thereafter and
                    ending on the 2000 Equipment Maturity Date, whereupon all
                    Equipment Advances under the 2000 Committed Equipment Line,
                    together with all accrued and unpaid interest thereon, shall
                    be due and payable in full. Equipment Advances, once repaid,
                    may not be reborrowed.

                    (c)  When Borrower desires to obtain an Equipment Advance,
                    Borrower shall notify Bank (which notice shall be
                    irrevocable) by facsimile transmission to be received no
                    later than 3:00 p.m. Eastern time one (1) Business Day
                    before the day on which the Equipment Advance is to be made.
                    Such notice shall be substantially in the form of Exhibit B.
                    The notice shall be signed by a Responsible Officer or its
                    designee and include a copy of the invoice for the Equipment
                    to be financed."

                    (d)  In the event the Borrower prepays in whole Equipment
                    Advances made under the 2000 Committed Equipment Line, the
                    Borrower shall be additionally obligated to the Bank for a
                    prepayment fee equal to (i) Twenty Thousand Dollars
                    ($20,000.00) if the 2000 Committed Equipment Line is prepaid
                    on or before December 22, 2001, and (ii) Ten Thousand
                    Dollars ($10,000.00) if the 2000 Committed Equipment Line is
                    prepaid after December 22, 2001 but on or before December
                    22, 2003.

                    (e)  In addition to any other fee to be paid by Borrower on
                    account of the 2000 Committed Equipment Line, the Borrower
                    shall pay Bank an "Unused Line Fee"  (so referred to herein)
                    of one quarter of one percent (0.25%) of the difference
                    between the full amount of the 2000 Committed Equipment Line
                    and the outstanding principal balance of all Equipment
                    Advances under the 2000 Committed Equipment Line as of the
                    2000 Equipment Availability End Date (or, if earlier, as of
                    the date of any prepayment of the Obligations as
                    specifically provided in Section 2.1.5(d)), as determined
                    solely and exclusively by Bank.  The Unused Line Fee shall
                    be paid on the 2000 Equipment Availability End Date, or, if
                    earlier, on the date of any prepayment of the Obligations as
                    specifically provided in Section 2.1.5(d).  The Borrower
                    shall not be entitled to any credit, rebate or repayment of
                    any Unused Line Fee previously earned by the Bank pursuant
                    to this Section notwithstanding any termination of the
                    within Agreement, or suspension or termination of the Bank's
                    obligation to make loans and advances hereunder."


          5.   The Loan Agreement shall be amended by deleting Section 6.3 in
               its entirety and inserting in lieu thereof the following:

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<PAGE>

                    "6.3  Financial Statements, Reports, Certificates.  Borrower
                          -------------------------------------------
                    shall deliver to Bank:  (a) as soon as available, but in any
                    event within forty-five (45) days after the end of each
                    quarter, a company prepared consolidated balance sheet and
                    income statement covering Borrower's consolidated operations
                    during such period, in a form and certified by an officer of
                    Borrower reasonably acceptable to Bank; (b) as soon as
                    available, but in any event within one hundred twenty (120)
                    days after the end of Borrower's fiscal year, audited
                    consolidated financial statements of Borrower prepared in
                    accordance with GAAP, consistently applied, together with an
                    unqualified opinion on such financial statements of an
                    independent certified public accounting firm reasonably
                    acceptable to Bank; (c) promptly upon receipt of notice
                    thereof, a report of any legal actions pending or threatened
                    against Borrower or any Subsidiary that could result in
                    damages or costs to Borrower or any Subsidiary of One
                    Hundred Thousand Dollars ($100,000) or more; and (d) such
                    budgets, sales projections, operating plans or other
                    financial information as Bank may reasonably request from
                    time to time.

                    Within forty-five (45) days after the last day of each
                    quarter and within one hundred twenty (120) days after the
                    end of Borrower's fiscal year, Borrower shall deliver to
                    Bank, with the financial statements required herein, a
                    Compliance Certificate signed by a Responsible Officer in
                    substantially the form of Exhibit D hereto.
                                              ---------

                    Within thirty (30) days after the end of each month,
                    Borrower shall deliver to Bank a written certification in
                    form and substance satisfactory to Bank, signed by a
                    Responsible Officer, confirming Borrower's compliance with
                    the minimum cash requirement set forth in Section 6.9
                    herein.

                    Bank shall have a right from time to time hereafter to audit
                    Borrower's Accounts at Borrower's expense, provided that
                    such audits will be conducted no more often than every
                    twelve (12) months unless an Event of Default has occurred
                    and is continuing."

          6.   The Loan Agreement shall be amended by deleting Sections 6.8
               (entitled "Adjusted Quick Ratio") and 6.9 (entitled "Tangible Net
               Worth) in their entirety and inserting in lieu thereof the
               following:

                    "6.9  Minimum Cash Requirement.  Borrower shall maintain, as
                          ------------------------
                    of the last day of each month, minimum cash on hand (and
                    cash equivalents) of at least Thirty Million Dollars
                    ($30,000,000.00), as determined solely by Bank.

                    6.9  Intentionally Omitted."
                         ----------------------

          7.   Without limiting the generality of Borrower's ratification herein
               of all Existing Loan Documents, the Borrower hereby ratifies,
               confirms and reaffirms, all and singular, the terms and
               conditions of a certain Negative Pledge Agreement dated as of
               November 5, 1997 between Borrower and Bank, and acknowledges,
               confirms and agrees that said Negative Pledge Agreement is and
               shall remain in full force and effect.

          8.   The Compliance Certificate appearing as Exhibit D to the Loan
                                                       ---------
               Agreement is hereby replaced with the Compliance Certificate
               attached as Exhibit A hereto.
                           ---------

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<PAGE>

4.   FEE. Borrower shall pay to Bank on demand all fees (including all
     ---
attorneys' fees), costs, and expenses incurred by Bank in connection with the
execution and delivery of this Third Modification Agreement.

5.   CONSISTENT CHANGES. The Existing Loan Documents are hereby amended wherever
     ------------------
necessary to reflect the changes described above.

6.   RATIFICATION OF LOAN DOCUMENTS. Borrower hereby ratifies, confirms, and
     ------------------------------
reaffirms all terms and conditions of all security or other collateral granted
to the Bank, and confirms that the indebtedness secured thereby includes,
without limitation, the Indebtedness.

7.   NO DEFENSES OF BORROWER. Borrower agrees that, as of this date, it is not
     -----------------------
aware of any defenses against the obligations to pay any amounts under the
Indebtedness.

8.   CONTINUING VALIDITY. Borrower understands and agrees that in modifying the
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existing Indebtedness, Bank is relying upon Borrower's representations,
warranties, and agreements, as set forth in the Existing Loan Documents. Except
as expressly modified pursuant to this Third Loan Modification Agreement, the
terms of the Existing Loan Documents remain unchanged and in full force and
effect. Bank's agreement to modifications to the existing Indebtedness pursuant
to this Third Loan Modification Agreement in no way shall obligate Bank to make
any future modifications to the Indebtedness. Nothing in this Third Loan
Modification Agreement shall constitute a satisfaction of the Indebtedness. It
is the intention of Bank and Borrower to retain as liable parties all makers of
Existing Loan Documents, unless the party is expressly released by Bank in
writing. No maker will be released by virtue of this Third Loan Modification
Agreement.

9.   JURISDICTION/VENUE. Borrower accepts for itself and in connection with its
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properties, unconditionally, the non-exclusive jurisdiction of any state or
federal court of competent jurisdiction in the Commonwealth of Massachusetts in
any action, suit, or proceeding of any kind against it which arises out of or by
reason of this Third Loan Modification Agreement; provided, however, that if for
any reason Bank cannot avail itself of the courts of the Commonwealth of
Massachusetts, then venue shall lie in Santa Clara County, California.

10.  COUNTERSIGNATURE. This Third Loan Modification Agreement shall become
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effective only when it shall have been executed by Borrower and Bank (provided,
however, in no event shall this Third Loan Modification Agreement become
effective until signed by an officer of Bank in California).

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<PAGE>

     This Third Loan Modification Agreement is executed as a sealed instrument
under the laws of the Commonwealth of Massachusetts as of the date first written
above.

BORROWER:                               BANK:

CENTRA SOFTWARE, INC.                   SILICON VALLEY BANK, doing business as
                                        SILICON VALLEY EAST


By:__________________________      By:____________________________

Name:________________________      Name:__________________________

Title:_______________________      Title:_________________________


                                        SILICON VALLEY BANK

                                        By:__________________________

                                        Name:________________________

                                        Title:_______________________
                                        (signed in Santa Clara County,
                                         California)

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<PAGE>

                                   EXHIBIT A

                            COMPLIANCE CERTIFICATE

TO:    SILICON VALLEY BANK

FROM:  CENTRA SOFTWARE, INC.

     The undersigned authorized officer of CENTRA SOFTWARE, INC. hereby
certifies that in accordance with the terms and conditions of the Loan and
Security Agreement between Borrower and Bank (the "Agreement"), (i) Borrower is
in complete compliance for the period ending ______________ with all required
covenants except as noted below and (ii) all representations and warranties of
Borrower stated in the Agreement are true and correct in all material respects
as of the date hereof. Attached herewith are the required documents supporting
the above certification. The Officer further certifies that these are prepared
in accordance with Generally Accepted Accounting Principles (GAAP) and are
consistently applied from one period to the next except as explained in an
accompanying letter or footnotes. The Officer expressly acknowledges that no
borrowings may be requested by the Borrower at any time or date of determination
that Borrower is not in compliance with any of the terms of the Agreement, and
that such compliance is determined not just at the date this certificate is
delivered.

 Please indicate compliance status by circling Yes/No under "Complies" column.

<TABLE>
<CAPTION>

     Reporting Covenant                       Required                                Complies
     ------------------                       --------                                --------
     <S>                                      <C>                                     <C>
     Quarterly financial statements           Quarterly within 45 days                 Yes  No
     Quarterly CC                             Quarterly within 45 days                 Yes  No
     Monthly Certification of Cash Balance    Monthly within 30 days                   Yes  No
     Annual (CPA Audited)                     FYE within 120 days                      Yes  No

     Financial Covenant                       Required                  Actual        Complies
     ------------------                       --------                  ------        --------

     Maintain:

     Minimum Cash Requirement (monthly)       $30,000,000.00            $_______       Yes  No

</TABLE>
                                                ================================
                                                            BANK USE ONLY
                                                Received By:____________________
Comments Regarding Exceptions:                  Date:________________
                                                Reviewed By:____________________
Sincerely,                                      Compliance Status:  Yes / No
                                                ================================
_______________________   Date:_______________
Signature
________________________
Title

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