All 260 holders of the Scottish posts who deal directly with customers were told at a meeting yesterday their jobs are at risk.
The Edinburgh bank, which is part-owned by the taxpayer, is looking to reduce an estimated £1 billion of costs after years of massive losses.
The shake-up involves the scrapping of the title of deputy manager. RBS plans to get rid of 58 manager or deputy manager posts from its 291 branches.
Executives have given those affected two weeks to consider whether they want to seek jobs in the new structure, seek redeployment, or take voluntary redundancy.
It is thought the move may be the prelude for a similar branch management restructure in RBS and NatWest branches south of the Border.
The move has come just five days after the 81% taxpayer-owned bank reported a jump in first quarter profits to £1.6bn from £826 million a year ago. Its troubled Ulster Bank - into which it has poured at least £14bn since the banking crisis - has also made a return to profit for the first time in five years.
The RBS figures contrasted with an £8.7bn full-year loss in 2013.
About 40,000 workers have already lost their jobs since RBS was bailed out with £45bn of taxpayers' money in 2008.
RBS says the latest move is about "taking out layers of manager to make it simpler and easier to do business with us" and will mean some smaller branches will no longer have an on-site manager. Towns that have more than one branch may share a manager.
A spokeswoman said: "All our branches will continue to have a branch manager. This change will not affect how we serve our customers. This is clearly difficult news for staff affected by these changes. We will do everything we can to support them, including seeking redeployment opportunities wherever possible and ensuring compulsory redundancies are kept to a minimum."
RBS said it also intended to create 10 customer service officer roles with those taken on answering to the branch managers.
In January this year, it emerged RBS was preparing to cut thousands more jobs as it looked to reduce an estimated £1bn of costs.
Two months later, the company said it planned to shut three branches - Chirnside, Greenlaw and Newtown St Boswells in the Borders - due to low usage.
Borders MSP John Lamont said he was "deeply disappointed" by the move, which would "adversely affect" RBS customers in the region.