A quarter of the total pay-out – which could net chief executive Stephen Hester a maximum 4.8 million – is linked to the RBS share price, which has risen strongly in recent weeks.
Two months ago, RBS shares were around 30p but they have now risen sharply to above 50p – potentially triggering the award of 30% of this part of the scheme, worth around 360,000 to the RBS boss.
Although the 50p mark represents the break-even mark for the taxpayer, who owns 83%, the award has angered some investors who have seen shares slump and dividends scrapped since the bail-out of the bank.
Sir Philip Hampton told shareholders at the firm's annual meeting that when the new scheme was finalised, "the share price was sitting at a much lower level than it is today".
"The remuneration committee is very conscious of the views expressed by some shareholders on the appropriateness of this target, given the recent strength in the share price, and I can confirm that the committee will take these views into account before finalising the target," he said.
Despite Sir Philip's pledge to review targets under the three-year scheme, PIRC – an organisation which advises institutional investors – said there were "still issues" with pay practices at the bank.
"The proposed long-term incentive plan is considered to have an excessive maximum pay-out of 400% and there is committee discretion to raise this level in 'exceptional circumstance'," PIRC said.
UK Financial Investments, which represents the taxpayer's stake in the banks, supported the new bonus scheme although it said all measures "must be appropriately stretching".
"We welcome the remuneration committee's assurances that the vesting schedule for the absolute share price measure will take appropriate account of the movement in share price since the beginning of the year," it added.
Sir Philip said he understood public concern over pay but added that it was "essential" that talented staff did not feel disadvantaged by working for RBS.
RBS has gone further than other banks on G20 pay practices such as deferral and clawback of bonuses and he said it had struck an "appropriate balance" over pay.
The bank does not reveal its first-quarter performance until 7 May, but shares have risen on recent upbeat broker comments on prospects for a recovery.
RBS and other banks have also come under attack from politicians in the General Election campaign for not lending enough, although the bank said it was making new loans to more than 5,000 small businesses every week.
The chairman said many firms were looking to reduce borrowing in the downturn, adding: "I would say that we need to have our eyes wide open about the reality of credit demand as we pull out of the recession.
"The political imperative of stretching targets is understood but, although we will make the money available, we cannot invent credit demand."
Although the economic outlook has improved upon a year ago, the chairman added that "we are under no illusions that we are out of the woods".
But Sir Philip added that the recent improvement in RBS's performance gave him confidence that the firm would go "a long way down the road towards leaving the 'problem bank' label behind" during the next year.