Permanent TSB is contacting some of its buy-to-let mortgage customers who are in arrears to see if they would surrender the property to the bank for sale.
The bank would then write off any remaining debt on the loan.
PTSB said that for customers who are offered and who agree to a "voluntary surrender", it will clear any arrears or shortfalls that remain on the loan after the property has been sold.
The bank added that it will not seek any further repayment by the borrowers in respect of the buy-to-let mortgage.
The scheme is restricted to only certain buy-to-let mortgages and follows a detailed review of the bank's non-performing loans. It is believed the initiative will be offered to a "few hundred" customers.
Permanent TSB, which is 75% owned by the State, is the first of the main banks here to offer such an initiative.
In July, the bank had said the number of non-performing loans on its books remained "unsustainably high". Its bad debts account for 28% of its loan book.
"The offer is limited to customers who the bank believes have no means of meeting the repayment terms of the loan or the shortfall debt which will arise upon the sale of the property," Permanent TSB said in today's statement.
The move followed recent comments by the bank's group chief executive, Jeremy Masding who said the bank would pursue a number of actions to deal with non-performing loans.
"While this current initiative is limited in scope, it is one of a number of initiatives which we are pursuing to reduce the number of non-performing loans at the bank. We believe it merits serious consideration by those customers who are invited to participate," a spokesman for PTSB said.