The Exeter branch of Britannia is set to close.
The Co-operative Bank today announced that the St Thomas branch is one of the 37 that will close.
The Britannia name will disappear from the High Street and be replaced by The Co-operative Bank as part of a merger.
Roughly 34 jobs will be lost across the county with most staff being relocated to nearby branches.
The current Britannia branch is located on Cowick Street with the nearest Co-operative Bank located on the High Street.
Other branches closing include two in Bristol and one in Torquay.
Co-operative Bank retail￼ banking managing director John Hughes said:
"We are now at the final stages of this integration and have carried out a review of our branch network to ensure that it meets the needs of our customers and is operating in the most efficient￼ and cost-effective way.
"We have identified a number of locations where we have bank branches in extremely close proximity and have taken the decision to merge branches in these locations, which will result in the closure of 37 branches."