Ulster Bank is to extend the deadline for those customers whose accounts are due to become non-operational later this week by a further month.
The bank says the move is to avoid unnecessary worry or complexity for customers in receipt of one-off and additional social welfare payments announced in the Budget last week.
The additional child benefit payment is due to be paid by November 1.
As a result, the first accounts that were due to become non-operational on October 8, will now not become so until or after November 4.
Non-operational means the account becomes frozen to transactions and is closed 30 days later.
"It is the right thing to do, to ensure that there are no unintended impacts on customers in receipt of these particular payments," Ulster Bank said in a statement.
"During this time, customers should continue to take steps to move or close their accounts," the lender added.
In April, Ulster Bank - which is currently undertaking a phased withdrawal from the Republic of Ireland market - began writing to customers to give them six months' notice to move their accounts to other lenders and close them.
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It claims that of those who received their first formal notification in April and May, 64% have now either closed or wound down their current account or left it approaching an inactive or dormant state.
"Ulster Bank is continuously reaching out to the remaining one third of these customers and most are reporting that they have opened a new account elsewhere and are in the process of moving their payments to their new account," it said.
It says that over 75% of its personal current account customers who receive social welfare payments have already taken action on their accounts.
Today's announcement follows another session today that was held with advocates for personal customers in vulnerable situations and advocates for older customers.
"As a bank, we have worked very hard to reach out to our customers to ensure that they are aware of their individual notice period and what will happen next, avoiding any surprises for them," Ulster Bank's chief executive Jane Howard said.
"It is crucial for all customers to understand that their notice to Choose-Move-Close still stands and they do need to take action on their current and deposit accounts when they receive their notice from us," the CEO said.
"As we move to this critical point, I reiterate our commitment to withdraw on a phased and orderly basis and today's announcement is in line with this commitment," she added.
