Nationwide said the charitable donation would be in very limited circumstances and only if customers don't have another current account with the bank to which they can pay the money.
Nationwide currently charges customers £20 to send large amounts of money between UK bank accounts but it said from May it will lower this to £15.
Four major changes hitting key Nationwide accounts in just months NATIONWIDE will make a number of changes to its key accounts in a matter of months.
If you have a current account with Nationwide and it closes, the bank said from May it could pay whatever small amount is left over to a charity.
Meanwhile, Nationwide's FlexDirect account pays customers interest on the money they have lodged in the account.