Ulster Bank has said its services are back to normal after customers last night reported problems withdrawing cash at ATMs and cards being declined.
There were also reports of Ulster Bank customers having problems accessing their accounts online or by telephone.
Ulster Bank said: "We are disappointed that our customers faced disruption to banking services for a period yesterday evening, and apologise for that.
"All services are now running as normal again."
Customers who are still experiencing problems can contact the bank on 1800-205100 (ROI) and 0800-231232 (NI).
It is understood the technical problems were part of a wider problem in Britain that affected the RBS banking group and its subsidiary NatWest.
The Consumers' Association of Ireland said the latest technical problems at the bank raise serious concerns for customers.
CAI Chief Executive Dermott Jewell said the bank is not delivering an adequate service.
Mr Jewell said: "It affected quite a significant number of people yesterday who needed to access the system to download money, to take care of their banking needs and they couldn't.
"And realistically it needs to be borne in mind that they're paying for this service and it's just not up to scratch.
"If we hark back to June there, the lessons from then do not seem to have been made clear to the customers of Ulster Bank to explain what has happened, what has been put in place to make sure there's a system that's robust."
Last summer, computer faults caused disruption for many Ulster Bank customers for a number of weeks.
RBS, NatWest and Ulster Bank had to extend opening hours at their branches to assist customers who had been unable to pay bills, move money or whose salaries had not been paid.
That problem was reported to be caused by an update to the software used for processing payments.