The bank has not been named yet but an application to the US authorities is being submitted.

The arrangement will see Dr Robertson holding a substantial minority stake.

Dr Robertson is well known in the USA as a religious broadcaster, entrepreneur and right wing politician who ran unsuccessfully for the US presidency in 1988.

Sainsbury model

The model for the venture is Sainsbury's Bank, which the bank launched in 1997 with the UK supermarket group.

The Bank of Scotland developed its expertise through a UK supermarket

Direct telephone banking is less developed in the US than in the UK, where operations such as First Direct have become part of the landscape of personal banking.

Dr Robertson's Christian Broadcasting Network reaches 55m viewers a year in the US.

Filing papers

The application to set up the new bank will be filed with the Office of the Comptroller of the Currency, the Federal Reserve Board of New York and the Federal Deposit Insurance Corporation.

The Bank of Scotland confirmed the US operation, which has not yet been named, will be a subsidiary of Bank of Scotland with Dr Robertson having a substantial minority interest.

Telephone banking is less developed in the US

Marshall & Ilsley (M & I) Corporation, a bank holding company based in Wisconsin, will provide the support services infrastructure, operational personnel and processing technologies for the new bank.

Peter Burt, Group Chief Executive, Bank of Scotland said: "The telephone and the computer are transforming the financial landscape.

"As we have seen in the UK, the opportunities to provide customers with top class service and products through direct channels are increasing by the day. "

Dr Pat Robertson added: "It is a very nice coincidence that my forebears left Scotland in 1695, the year in which Bank of Scotland was founded."

More details of the new bank's identity operations and marketing strategy will be released when the bank is launched.

Dr Robertson recently joined the board of the struggling Laura Ashley group.