Royal Bank of Scotland chairman Sir Philip Hampton has given up a £1.4m shares reward he was due next month.
Sir Philip told the bank's remuneration committee it would not be appropriate to receive the 5.17 million shares, says the BBC's Robert Peston.
Meanwhile, the government said it would not block a £963,000 bonus, also in shares, for RBS chief Stephen Hester.
Prime Minister David Cameron said it was up to Mr Hester whether he accepted the bonus.
"That's a matter for him, that's obviously his decision."
Mr Hester's contract at RBS - which is 82% publicly owned - was agreed by the last Labour government, Mr Cameron said.
The prime minister said alternatives - such as bringing in a new team at RBS - "could be even more expensive".
"We need this team to get on with the job of turning the bank around, making it safe and securing for the British taxpayer - getting back - all the money that was put into RBS."
RBS has confirmed Sir Philip's decision not to accept his shares reward.
But sources have told the BBC his bonus was agreed three years ago when he became chairman in recognition for the scale of the task of turning around the bank.
The BBC's Robert Peston said Sir Philip made his decision before the uproar over Mr Hester's payment, which is still drawing criticism.
Labour leader Ed Miliband accused Mr Cameron and his government of being out of touch for failing to block the chief executive's share bonus.
Mr Miliband told the BBC that Mr Hester had done a "decent" job but that most people would think that his £1.2m salary was enough.
At a bank that was 83% state owned, there had to be some kind of "equality of sacrifice," he said.
In a written statement released earlier on Saturday, Mr Miliband said: "Freezing the pay of a nurse or hospital porter, while allowing a publicly-owned bank to pay million-pound bonuses, is the last nail in the coffin of this prime minister's claim that we're all in it together.
He said his message to Mr Cameron was: "You've got another chance. At the AGM in April the government, as the majority shareholder in RBS, will have to decide how to vote on the bonus. They should vote it down."
Liberal Democrat deputy leader Simon Hughes said Sir Philip had set the right example and that "all those on the boards and in senior management at RBS and LloydsTSB should now act with equal principle and social awareness".
"In these days of austerity above all, it is unacceptable for anybody whose business has depended on public funds to take bonuses or salaries at levels which many tax payers regard as obscene" Mr Hughes said.
Professor Chris Roebuck of Cass Business School in London says there is little the government can do about pay and bonuses at RBS, because they are determined by overseas banks.
"In London there are 23 international banks, of which only three are British," he said.
"Pay levels in London are determined by those other 20 overseas banks who determine their pay on what's happening globally, and if the British banks don't play along and if RBS doesn't play along, all it means is that somebody who works for RBS has to walk 50 yards across the street to Deutsche Bank to get more money."
The pay award sparked anger across the political spectrum with one Lib Dem minister calling for Mr Hester to waive the payment and the Mayor of London, Conservative Boris Johnson, urging the government to "step in".
But No 10 has said the proper processes were followed and it was up to Mr Hester to decide whether to accept
The contract agreed in 2009 meant Mr Hester was entitled to be considered for a bonus, a spokesman said.
"That process was established by the previous government and that process is reflected in a bonus which is less than half the bonus Stephen Hester was paid last year.
"The public sector shareholder has taken a keen interest in this and has had an influence on it."
The bonus is not payable for three years, when the final amount will be determined by the firm's share price.
Several City and business analysts have said Mr Hester is entitled to receive a bonus for his performance.