Bank of Ireland is refunding €1.3m to 14,000 customers this week.
The bank says It is in lieu of the fact that some customers were not refunded their money, after they did not take their cash from an ATM.
If their account was debited for the amount, then Bank of Ireland will refund the customers the amount.
A further €1.7m will also be refunded to 29,000 non-Bank of Ireland customers who were affected, through their own banks.
The issue arose following the installation of anti-fraud measures at the bank.