The Paisley Central branch will shut on May 7, meaning its only town base will be in Moncrieff Street, a half-mile walk from the town's High Street.
The shutters came down on its Paisley Eastern branch in Glasgow Road after some 50 years in March last year.
RBS, which is majority-owned by the taxpayer, said it took the "difficult decision" to close the town centre branch in St Mirren Street, which has been in existence for decades as the numbers using the branch had fallen "significantly" over the past few years.
It said customers were choosing alternative ways of banking through the internet, mobile phone apps and telephone.
Paisley and Renfrewshire South Labour MP Douglas Alexander criticised RBS for making the move without any customer consultation.
He said: "RBS has let local people down by its decision to close the central branch.
"Many elderly customers in particular rely on easy access to their branch, but RBS has decided to force this closure upon them."
RBS said the number of customers using the branch had dropped by 15 per cent.
An RBS spokesman said: "We've seen the number of people using the branch fall significantly over the last few years and we've made the difficult decision to close the Paisley Central branch."