Exhibit (a)(1)(H)

This announcement is neither an offer to purchase nor a solicitation of an offer
to sell Shares. The Offer is made solely pursuant to the Offer to Purchase,
dated October 24, 2000, and the related Letter of Transmittal (and any
amendments or supplements thereto), and is being made to all holders of Shares.
Purchaser is not aware of any state where the making of the Offer is prohibited
by administrative or judicial action pursuant to any valid state statute. If
Purchaser becomes aware of any valid state statute prohibiting the making of the
Offer or the acceptance of the Shares pursuant thereto, Purchaser shall make a
good faith effort to comply with such statute or seek to have such statute
declared inapplicable to the Offer. If, after such good faith effort, Purchaser
cannot comply with such state statute, the Offer will not be made to (nor will
tenders be accepted from or on behalf of) holders of Shares in such state. In
any jurisdiction where the securities, "blue sky" or other laws require the
Offer to be made by a licensed broker or dealer, the Offer shall be deemed to be
made on behalf of Purchaser by Deutsche Bank Securities Inc. (the "Dealer
Manager") or one or more registered brokers or dealers licensed under the laws
of such jurisdiction.


                     Notice of Offer to Purchase for Cash

                    All Outstanding Shares of Common Stock

                                      of

                     National Discount Brokers Group, Inc.

                                      at

                             $49.00 Net Per Share

                                      by

                          Deutsche Acquisition Corp.

                    An indirect wholly owned subsidiary of

                               Deutsche Bank AG

        Deutsche Acquisition Corp., a Delaware corporation ("Purchaser") and an
indirect wholly owned subsidiary of Deutsche Bank AG, a banking company with
limited liability organized under the laws of the Federal Republic of Germany
("Parent"), hereby offers to purchase all outstanding shares of common stock,
par value $.01 per share ("Shares"), of National Discount Brokers Group, Inc., a
Delaware corporation (the "Company"), that are not already beneficially owned by
Parent at a purchase price of $49.00 per Share, net to the seller in cash (less
any required withholding taxes), without interest thereon, upon the terms and
subject to the conditions set forth in the Offer to Purchase, dated October 24,
2000 (the "Offer to Purchase"), and in the related letter of transmittal (the
"Letter of Transmittal," which together with the Offer to Purchase, as amended
or supplemented from time to time, collectively constitute the "Offer").

- --------------------------------------------------------------------------------
THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY
TIME, ON TUESDAY, NOVEMBER 21, 2000, UNLESS THE OFFER IS EXTENDED.
- --------------------------------------------------------------------------------

        The Offer is being made pursuant to an Agreement and Plan of Merger,
dated as of October 11, 2000, as amended (the "Merger Agreement"), among Parent,
Purchaser and the Company pursuant to which, after completion of the Offer and
the satisfaction or waiver of certain conditions, Purchaser will be merged with
and into the Company (the "Merger") with

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the Company continuing as the surviving corporation and as an indirect wholly
owned subsidiary of Parent. At the effective time of the Merger (the "Effective
Time"), each Share issued and outstanding immediately prior to the Effective
Time (other than any Shares held by Parent, Purchaser, any direct or indirect
wholly owned subsidiary of Parent or Purchaser, in the treasury of the Company
or by any wholly owned subsidiary of the Company) will be converted into the
right to receive $49.00 in cash, without interest, or any higher price that is
paid in the Offer (less any withholding taxes required under applicable law).
The Merger Agreement is more fully described in the Offer to Purchase.

        Simultaneously with the execution of the Merger Agreement, Purchaser
entered into a Stockholder Tender Agreement, dated as of October 11, 2000 (the
"Stockholder Tender Agreement"), with certain principal stockholders of the
Company who currently hold an aggregate of 6,113,882 Shares (not including
Shares subject to options), representing approximately 29.1% of the Shares on a
fully diluted basis. Pursuant to the Stockholder Tender Agreement, the principal
stockholders have agreed, among other things, to tender all such Shares pursuant
to the Offer and have agreed to vote such Shares in favor of the Merger. The
Stockholder Tender Agreement is more fully described in the Offer to Purchase.

        The Offer is conditioned upon, among other things, there being validly
tendered and not properly withdrawn prior to the expiration of the Offer that
number of Shares which, together with the Shares then beneficially owned by
Purchaser or Parent or any of their respective affiliates, represents at least a
majority of the total number of outstanding Shares on a fully diluted basis (the
"Minimum Tender Condition"). Parent currently beneficially owns approximately
16.7% of the outstanding Shares. Accordingly, assuming the principal
stockholders tender all their Shares, Purchaser believes that the Minimum Tender
Condition would be satisfied if at least approximately 1,835,102 additional
Shares are validly tendered prior to the Expiration Date (as defined below) and
not properly withdrawn. The Offer is also subject to the other conditions set
forth in the Offer to Purchase. See Section 12, "Certain Conditions of the
Offer," of the Offer to Purchase.

        The Board of Directors of the Company (other than Parent's
representative, who was absent and did not vote) unanimously approved the Offer
and the Merger and determined that the Merger Agreement and the transactions
contemplated therein, including the Offer and the Merger, are advisable and fair
to, and in the best interests of, the Company's stockholders (other than Parent
and its wholly owned subsidiaries) and recommends that such stockholders accept
the Offer and, if stockholder approval of the Merger is required by law, vote
for the approval and adoption of the Merger Agreement.

        Stockholders of record who tender directly to the Depositary (as defined
below) will not be obligated to pay brokerage fees or commissions or, subject to
Instruction 6 of the Letter of Transmittal, stock transfer taxes, if any, on the

                                       2


purchase of Shares by Purchaser pursuant to the Offer. Stockholders who hold
their Shares through a broker or bank should consult such institution as to
whether it charges any service fees. Purchaser will pay all charges and expenses
of the Dealer Manager, ChaseMellon Shareholder Services, L.L.C., which is acting
as depositary (the "Depositary"), and Georgeson Shareholder Communications Inc.,
which is acting as the information agent (the "Information Agent"), incurred in
connection with the Offer.

        For purposes of the Offer, Purchaser will be deemed to have accepted for
payment, and thereby purchased, Shares validly tendered to Purchaser and not
properly withdrawn if, as and when Purchaser gives oral or written notice to the
Depositary of Purchaser's acceptance of such Shares for payment pursuant to the
Offer. Upon the terms and subject to the conditions of the Offer, payment for
Shares purchased pursuant to the Offer, including during any subsequent offering
period, will be made by deposit of the purchase price therefor with the
Depositary, which will act as agent for tendering stockholders for purposes of
receiving payment from Purchaser and transmitting payment to tendering
stockholders. Under no circumstances will interest be paid on the purchase price
for Shares, regardless of any extension of the Offer or any delay in making such
payment. In all cases, payment for Shares accepted for payment pursuant to the
Offer will be made only after timely receipt by the Depositary of (i)
certificates representing Shares (the "Share Certificates") or timely
confirmation of the book-entry transfer of such Shares into the Depositary's
account at The Depository Trust Company ("DTC") pursuant to the procedures set
forth in Section 3, "Procedures for Tendering Shares," of the Offer to Purchase,
(ii) the Letter of Transmittal (or a manually signed facsimile thereof),
properly completed and duly executed, with any required signature guarantees or
an Agent's Message (as defined in the Offer to Purchase) in connection with a
book-entry transfer of Shares, and (iii) any other documents required by the
Letter of Transmittal.

        If any of the conditions set forth in the Offer to Purchase that relate
to Purchaser's obligations to purchase the Shares are not satisfied by 12:00
Midnight, New York City time, on Tuesday, November 21, 2000 (or any other time
then set as the Expiration Date), Purchaser may, subject to the Merger Agreement
and any applicable rules and regulations of the Securities and Exchange
Commission (the "SEC"), elect to (i) extend the Offer and, subject to applicable
withdrawal rights, retain all tendered Shares until the expiration of the Offer,
as extended, (ii) waive all unsatisfied conditions (other than the Minimum
Tender Condition) and accept for payment all tendered Shares and not extend the
Offer, (iii) terminate the Offer and not accept for payment any Shares and
return all tendered Shares to tendering stockholders or (iv) amend the Offer.
The term "Expiration Date" means 12:00 Midnight, New York City time, on Tuesday,
November 21, 2000, unless Purchaser shall have extended the period of time for
which the Offer is open, in which event the term "Expiration Date" shall mean
the latest time and date at which the Offer, as so extended by Purchaser, shall
expire.

        Subject to the terms and conditions set forth in the Offer to Purchase
and the provisions of the Merger Agreement

                                       3


and the applicable rules and regulations of the SEC, Purchaser expressly
reserves the right, in its sole discretion, at any time or from time to time, to
extend the period of time during which the Offer is open. During any such
extension, all Shares previously tendered and not properly withdrawn will remain
subject to the Offer, subject to the rights of a tendering stockholder to
withdraw such stockholder's Shares.

        Subject to the provisions of the Merger Agreement and the applicable
rules and regulations of the SEC, Purchaser also reserves the right, in its sole
discretion, at any time or from time to time, to: (1) terminate the Offer
(whether or not any Shares have previously been purchased pursuant to the Offer)
if any of the conditions referred to in Section 12, "Certain Conditions of the
Offer," of the Offer to Purchase has not been satisfied or earlier waived or
upon the occurrence of any event specified in such section; (2) waive any such
unsatisfied condition (other than the Minimum Tender Condition, which may only
be waived with the prior written consent of the Company); or (3) modify or amend
the terms and conditions of the Offer in any respect, in each case, by giving
oral or written notice of the termination, waiver or amendment to the
Depositary.

        Any extension, delay, termination or amendment of the Offer will be
followed as promptly as practicable by a public announcement. An announcement in
the case of an extension will be made no later than 9:00 a.m., New York City
time, on the next business day after the previously scheduled Expiration Date.

        In addition, following the Expiration Date (as it may be so extended)
and the purchase of Shares in the Offer, there may be a subsequent offering
period, lasting for at least three and not more than 20 business days;
stockholders who tender Shares during a subsequent offering period will not have
the right to withdraw their Shares during such subsequent offering period.
Purchaser does not currently intend to include a subsequent offering period,
although it reserves the right to do so in its sole discretion regardless of
whether or not the events or the facts set forth in Section 12, "Certain
Conditions of the Offer", of the Offer to Purchase have occurred. If Purchaser
shall have acquired less than 90% of the Shares on the Expiration Date of the
Offer, it intends to elect to provide a Subsequent Offering Period. Pursuant to
Rule 14d-7 under the Securities Exchange Act of 1934, as amended, no withdrawal
rights apply to Shares tendered during a Subsequent Offering Period and no
withdrawal rights apply during the Subsequent Offering Period with respect to
Shares tendered in the Offer and accepted for payment. The same consideration
will be paid to stockholders tendering Shares in the Offer or in a Subsequent
Offering Period, if one is included.

        Tenders of Shares made pursuant to the Offer are irrevocable, except
that Shares tendered pursuant to the Offer (except during any subsequent
offering period) may be withdrawn at any time on or prior to the Expiration Date
and, unless theretofore accepted for payment as provided in the Offer to
Purchase, may also be withdrawn at any time after December 22, 2000. In order
for a withdrawal to be effective, a written or facsimile transmission notice of
withdrawal must be timely received by the Depositary at one of its addresses set
forth on the back cover of the Offer to Purchase. Any such notice of

                                       4


withdrawal must specify the name of the person who tendered the Shares to be
withdrawn, the number of Shares to be withdrawn, and (if Share Certificates have
been tendered) the name of the registered holder of the Shares as set forth in
the Share Certificate, if different from that of the person who tendered such
Shares. If Share Certificates evidencing Shares to be withdrawn have been
delivered or otherwise identified to the Depositary, then prior to the physical
release of such certificates, unless the Shares have been tendered by an
Eligible Institution (as defined in the Offer to Purchase), the tendering
stockholder must submit the serial numbers shown on the particular certificates
evidencing the Shares to be withdrawn and the signature on the notice of
withdrawal must be guaranteed by an Eligible Institution. If Shares have been
tendered pursuant to the procedures for book-entry transfer as set forth in
Section 3, "Procedures for Tendering Shares," of the Offer to Purchase, any
notice of withdrawal must also specify the name and number of the account at the
appropriate Book-Entry Transfer Facility (as defined in the Offer to Purchase)
to be credited with the withdrawn Shares, in which case a notice of withdrawal
will be effective if delivered to the Depositary by any method of delivery
described in this paragraph. Withdrawals of Shares may not be rescinded. Any
Shares properly withdrawn will thereafter be deemed not validly tendered for
purposes of the Offer, but may be tendered at any subsequent time prior to the
Expiration Date by following any of the procedures described in Section 3,
"Procedures for Tendering Shares," of the Offer to Purchase. All questions as to
the form and validity (including time of receipt) of notices of withdrawal will
be determined by Purchaser, in its sole discretion, whose determination shall be
final and binding.

        The receipt of cash in exchange for Shares pursuant to the Offer (or the
Merger) will be a taxable transaction for U.S. federal income tax purposes and
may also be a taxable transaction under applicable state, local or foreign tax
laws. Generally, a stockholder who receives cash in exchange for Shares pursuant
to the Offer (or the Merger) will recognize gain or loss for U.S. federal income
tax purposes equal to the difference between the amount of cash received and
such stockholder's adjusted tax basis in the Shares exchanged therefor. Provided
that such Shares constitute capital assets in the hands of the stockholder, such
gain or loss will be capital gain or loss, and will be long-term capital gain or
loss if the holder has held the Shares for more than one year at the time of
sale. The maximum U.S. federal income tax rate applicable to individual
taxpayers on long-term capital gain is 20%, and the deductibility of capital
losses is subject to limitations. All stockholders should consult with their own
tax advisors as to the particular tax consequences of the Offer and the Merger
to them, including the applicability and effect of the alternative minimum tax
and any state, local or foreign income and other tax laws and of changes in such
tax laws. For a more complete description of certain U.S. federal income tax
consequences of the Offer and the Merger see Section 5, "Certain United States
Federal Income Tax Consequences of the Offer," of the Offer to Purchase.

                                       5


        The information required to be disclosed pursuant to Rule 14d-6(d)(1) of
the General Rules and Regulations under the Securities Exchange Act of 1934, as
amended, is contained in the Offer to Purchase, and is incorporated herein by
reference.

        The Company is providing Purchaser with the Company's stockholder list
and security position listings for the purpose of disseminating the Offer to
holders of Shares. The Offer to Purchase and the related Letter of Transmittal
and, if required, other relevant materials will be mailed to record holders of
Shares whose names appear on the stockholder list, and will be furnished to
brokers, dealers, commercial banks, trust companies and similar persons whose
names, or the names of whose nominees, appear on the stockholder list or who are
listed as participants in a clearing agency's security position listing for
subsequent transmittal to beneficial owners of Shares.

        The Offer to Purchase and the related Letter of Transmittal contain
important information which should be read carefully before any decision is made
with respect to the Offer.

        Questions and requests for assistance or for additional copies of the
Offer to Purchase, the Letter of Transmittal, the Notice of Guaranteed Delivery
or other tender offer materials may be directed to the Dealer Manager or the
Information Agent at their respective telephone numbers and addresses listed
below, and copies will be furnished at Purchaser's expense. Neither Parent nor
Purchaser will pay any fees or commissions to any broker, dealer or other person
other than the Depositary, the Dealer Manager and the Information Agent in
connection with soliciting tenders of Shares pursuant to the Offer.

                    The Information Agent for the Offer is:

                   Georgeson Shareholder Communications Inc.

                         17 State Street, 10 th Floor
                           New York, New York 10004
                Banks and Brokers Call Collect: (212) 440-9800
                   All Others Call Toll Free: (800) 223-2064

                     The Dealer Manager for the Offer is:

                           Deutsche Banc Alex. Brown
                         Deutsche Bank Securities Inc.
                        130 Liberty Street, 33 rd Floor
                           New York, New York 10006
                        Call Toll Free: (877) 305-4919


October 24, 2000

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