Royal Bank of Scotland bosses announced that they will close their Commercial Street branch on August 18.
It is the latest in a number of closure announcements by major banks, including the decision to close the Sowerby Bridge branch of Halifax.
Changes in the way customers do their banking was blamed by RBS bosses, who also confirmed that the company had developed technology enabling them to do their banking at the nearby NatWest.
A statement said: "The way people bank with us has changed radically over the last few years. Since 2014, branch transactions across Royal Bank of Scotland in England & Wales are down 30%. During the same period, there has been a 53% increase in the number of customers using mobile banking and mobile transactions have increased by 74%.
"Since 2012 we have seen the way in which people use Halifax branch change, with 73% of customers already banking in other ways locally. Transactions at Halifax have reduced by 48% since 2012 with only 48 customers now visiting the branch on a regular weekly basis."