Just over 94% of current accounts at exiting Ulster Bank and KBC are now closed, new figures from the Central Bank show.
As of the end of May, just 25,073 current accounts were deemed by the two banks as being a customer's 'primary' account.
42,743 current and deposit accounts were closed in the four weeks to the end of the month, significantly lower than the previous month.
The Central Bank said this reflects the reduced number of accounts that remain to be closed.
"This smaller cohort may include more challenging cases to settle," the Central Bank added.
However, the latest weekly closure figures remain significantly higher than the average number of closures recorded between 2018 and 2021.
The total number of accounts closed at the two banks since the beginning of last year stands at 1,133,524.
Across the main remaining retail banks - AIB, Bank of Ireland and Permanent TSB - 42,865 accounts were opened in the four weeks to end-May.
That figure is largely unchanged when compared with the previous month.
In total, 1,243,675 current and deposit accounts were opened across the three remaining retail banks since the beginning of last year.
