Bank of Scotland (Ireland) and Halifax have chosen not to join the Government's bank guarantee scheme.
In a statement, the bank said to join the scheme would not be in the best interests of their customers.
Halifax is Bank of Scotland's retail division in Ireland.
Earlier this month, the British government bought a substantial number of shares in Bank of Scotland as part of a £50bn rescue plan.
Bank of Scotland said this had strengthened it operations and by joining the Irish scheme it would be restricted in its ability to compete and offer new products to customers.
Chief executive Mark Duffy said that while the scheme had some merits and may suit some of Bank of Scotland's competitors, it would prevent Bank of Scotland from offering better deals.
On Saturday Minister for Finance Brian Lenihan signed an order confirming that the six main Irish owned banks are covered by the State's deposit guarantee scheme.
Those banks are AIB, Bank of Ireland, Anglo Irish Bank, EBS Building Society, Irish Life & Permanent and Irish Nationwide.