Deposits made with Bank of Ireland's Isle of Man arm will not fall under the Government guarantee scheme from August 10.
The Government is quoted as saying the move was part of the lender's efforts to cut its funding costs.
The bank in March withdrew its UK arm from the scheme and said it was progressing other initiatives to wean itself off the scheme.
Michael Noonan is quoted by the news agency Reuters as saying he had agreed to amend the rules of the guarantee scheme at the request of Bank of Ireland.
The Government issued a blanket guarantee for all bank liabilities in September 2008.
The blanket guarantee expired in September 2010 and the current guarantee, referred to as the ELG scheme, is narrower, covering bank deposits and certain liabilities up to a maximum maturity of five years.
