Some 6,000 staff at Bank of Ireland are in line for a 3.75% pay increase, part of which will be back-dated to July.
This is along with a 5% lump sum payment before Christmas.
It is the first widespread pay increase at any of the bailed out banks since 2008.
Bank of Ireland has repaid its bailout loans and is back in profitability - but the bank recently refused a cut to its variable mortgage rate holders.
The Finance Union (IBOA) says it is also in talks with AIB over a pay increase - but that these talks are at an early stage.
General-secretary of IBOA is Larry Broderick. He says the move is not a bonus payment for staff.