The Royal Bank of Scotland Group (RBS) has warned its UK staff that they must have their primary bank account with the firm or face disciplinary action.
Other leading banks also have the same account requirements
In a letter obtained by union Amicus, a senior executive told staff salaries must be paid into an RBS-run account.
"Failure to do so will represent a breach of group policy," it said.
The bank said its policy was in line with other leading banks but Amicus said it was taking legal advice, accusing RBS of "heavy-handedness".
Amicus said up to 14,000 RBS staff still maintained their primary accounts with competitors.
As well as Royal Bank of Scotland, RBS Group owns NatWest, Direct Line and Churchill Insurance.
RBS said it explained to all staff at their interviews that they would be required to hold an RBS Group-administered current account for the purpose of receiving their salaries.
It said this was part of the "overall reward package" on offer to staff.
"In common with industry practice, our terms and conditions require staff to open a current account with us for the payment of their salary," a spokeswoman said.
"Our staff are at complete liberty to run accounts with other providers if they wish."
One Royal Bank of Scotland member of staff told the BBC that the bank's action as "atrocious" and said it was "sapping morale".
The person pointed out that staff who worked for companies such as Direct Line and Churchill before they were taken over by RBS now faced disciplinary action if they did not comply with the account instruction.
"People in my office have all had it and they are all staff in excess of 10 years.
"It would never have been part of their original contract to have an RBS account. If it was, why has it taken 10 years to chase them on it?"
Stephen Cape, the BBC's Labour Affairs Correspondent, said unions were unhappy with the way the bank had handled the issue.
Amicus said it had been contacted by RBS staff unhappy about the requirement and urged the bank to reconsider its position.
"If you work for Tesco you won't be disciplined for buying your groceries from Sainsbury's," said official Rob Macgregor.
"RBS's disproportionate and heavy-handed approach is counterproductive and bad for morale."