Some Ulster Bank customers were unable to access their accounts for almost a month.
Last summer, computer faults caused weeks of disruption for thousands of Ulster Bank customers.
On Friday, Ulster Bank said it had handled 70, 000 calls in the past week.
Ulster Bank, the third-largest bank in Ireland, is owned by Royal Bank of Scotland (RBS).
However, customers of the Ulster Bank subsidiary witnessed the fallout affecting their accounts for even longer.
Last week, Ulster Bank announced details of a compensation scheme for customers who were affected.
The Ulster Bank has said it expects services to return to normal by Monday.
Mr Brown said Ulster Bank branches would remain on extended opening hours this week.
Ulster Bank has said normal service has been restored to the majority of its customers.
Normal service was not restored to Ulster Bank customers until almost a month later on 16 July.
William Higgins, of RBS, and Ulster Bank's head of retail banking, Stephen Cruise, also appeared before MLAs.
The availability of the new series was welcomed by Richard Ramsey, chief economist at the Ulster Bank.
The finance minister has criticised the ongoing delay for Ulster Bank customers getting access to their money.
The Ulster Bank currently has 146 branches in the Republic of Ireland and 90 in Northern Ireland.
The e-mail was obtained by the BBC, and was issued by internal communications at the Ulster Bank.
Twenty-two branches and sub-offices of the Ulster Bank are due to close across Ireland, the bank has confirmed.
Ulster Bank has 1.9m customers in Northern Ireland, the Irish Republic and other parts of the United Kingdom.
Customers seeking further information can go online, call into their local Ulster Bank branch or telephone 0800 231232.
However, Ulster Bank staff are still working through a backlog of uncompleted transactions.
The latest Royal Institution of Chartered Surveyors (RICS) and Ulster Bank Housing Market Survey showed a rise in transactions.
In a statement, Ulster Bank said that it would provide further details on the closures within the next few weeks.
Letters will be sent to customers of Ulster Bank, part of the RBS Group, from January that explains the change.
The Ulster Bank has been criticised for the continuing delay in compensating customers affected by a computer failure in June.
The glitch affected customers of RBS, NatWest and Ulster Bank, and prompted Mr Hester to hand back his bonus for 2012.
Thousands of Ulster Bank customers were unable to withdraw cash or access their accounts after a software upgrade on 19 June.
The computer failure affected the entire Royal Bank of Scotland (RBS) group, but Ulster Bank took longest to resolve the issue.
As a result of the crisis, the Ulster Bank's chief executive Jim Brown said he would forego his bonus for 2012.
Last month, the Ulster Bank announced details of a compensation scheme for customers who were affected by the major computer failure.
Its chief executive, Antoinette McKeown, said Ulster Bank had to ensure this redress scheme compensated affected customers quickly, fairly and consistently.
Normal service was not restored to Ulster Bank customers until 16 July.
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