The main impact is on Jersey where 26 positions are to go, compared to nine in the Isle of Man, three in Guernsey, and others in Gibraltar.
Further jobs are also at risk and include both senior management roles and clerical positions.
RBS said the cuts follow a strategic review announced by the company at the end of February.
RBS International CEO Adrian Gill said: "The intention is to make RBS a small, simpler and smarter bank that puts the needs of its customers at its core."
RBS International will continue to operate across Jersey, Guernsey, the Isle of Man and Gibraltar.
In a separate development last week, Kleinwort Benson said it was pulling out of the Isle of Man with 12 jobs affected in banking and wealth management services.
Kleinwort Benson was quoted as saying that while the island business remains profitable, it lacked critical mass and an orderly wind down of the business was to take place.
Clients will be given a smooth transition to a new service provider by the end of this year, it added.
