Ulster Bank has said over 100,000 people have been affected by a one-day delay in processing certain payments.
It said some payments to customers and Social Welfare claimants may not be paid until tomorrow as it continues to try to solve technical problems.
The fault, which emerged yesterday, also affected transactions at NatWest, its sister bank in Britain.
The bank said it is in the process of contacting those organisations affected and says concerned customers should check their website for updates.
Staff at Ulster Bank headquarters and at branches across the country spent much of yesterday dealing with complaints and queries from customers.
The bank's website was also affected, with internet customers informed that account balances were not up to date and online services were unavailable.
Around 80 Ulster Bank branches will stay open until 7pm tomorrow to assist customers.