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It is the biggest loss of jobs since BT announced it planned to cull 10,000 posts last November.
The bank's manufacturing division is expected to bear the brunt of the job cuts.
Scotland's finance minister, John Swinney, commented: "It is extremely disappointing news that RBS is consulting on a new business plan which could involve job losses in Scotland.
"This will obviously be a worrying time for employees."
The Unite trade union said that the bank, in which the taxpayer has a majority stake, must not be allowed to lose jobs.
Recently, more than 90 per cent of RBS shareholders voted to reject the bank's policy on pay and pensions.
It has also emerged that former chairman Sir Fred Goodwin has refused to reduce his pension on a voluntary basis.








