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The award - made under the bank's long-term incentive plan - is on top of a £2m annual bonus already confirmed by the group and Mr Hester's £1.2m salary.
He also stands to pick up six million shares as part of his 2011 maximum annual bonus.
Based on the current share price, these would be worth around £2.7m.
RBS has also revealed bonus payments for a raft of other executives at the bank, which is 83% owned by the taxpayer.
They include a £1.4m annual handout and potential £2.8m long-term incentive payout for finance boss Bruce Van Saun. >>> Graham Fitzgerald, Sky News Online | Tuesday, March 08, 2011