The Bank of Scotland (Ireland) and Halifax which are owned by British bank HBOS, will not tap into the Government's banking guarantee plan after the British government pledged to protect as much as £250 billion of bank debt in order to help unlock credit markets.
At the end of last month, the Government agreed to guarantee the deposits and borrowings of the State's biggest banks to bolster confidence.
The banks will pay €1 billion over two years to the Government in return.
"While the scheme has its merits, and it may suit some of our competitors to join,from our strong financial position it doesn't suit us," Mark Duffy, chief executive officer at Bank of Scotland (Ireland), said in a statement.
"It would ultimately prevent our ability to offer a better deal for our customers," Mr Duffy said.
Last week Mr Lenihan signed the order guaranteeing AIB, Bank of Ireland, Anglo Irish Bank, Irish Life Permanent, EBS and Irish Nationwide Building Society after receiving "guaranteed acceptance deeds" from the six lenders confirming that they wished to participate in the scheme.
The order covers AIB's subsidiaries in the UK and the Channel Islands, and AIB North America. Bank of Ireland and its subsidiary, ICS Building Society, are also guaranteed.
Anglo Irish Bank said in a statement that its branches in the UK, Jersey, Germany and Austria, and its international division based in the Isle of Man, also fell under the scheme.
The Isle of Man subsidiaries of Bank of Ireland, Irish Life Permanent (ILP) and Irish Nationwide are also covered. Mr Lenihan said in a statement that the guarantee gives "absolute comfort to depositors and investors that they have the full protection of the State".
Mr Lenihan said that strict conditions accompanying the guarantee would ensure that "in accordance with prudent banking practice, that risk is properly measured and managed, and the interest of taxpayers are safeguarded".
Yesteday banking sector analysts at Davy Research downgraded its earnings per share (eps) forecasts for the banks covered by the guarantee scheme by as much as 21 per cent for 2009 and by up to 14 per cent for 2010.
"We are also cutting all dividends to zero on the assumption that the Government will prefer to see banks improve solvency rather than remunerate shareholders," Davy analysts Scott Rankin and Niamh Hore said.
They also predicted that if the Government chooses to inject capital into the bank, it will seek some mergers in the sector first.