The government is to own 57.9% of Royal Bank of Scotland after shareholders bought only a tiny proportion of the new shares being offered by the bank.
The small take-up had been expected as the offer price of 65.5p was about 10p higher than the price at which the shares were trading.
The share issue by RBS, which owns NatWest, was part of the government's plan to recapitalise banks.
The government will pay about £15bn for the majority stake in the bank.
It will also buy £5bn of preference shares in the bank.
Existing shareholders agreed to buy almost 56 million shares, which represents just 0.24% of the new shares on offer, at a cost of £36.7m, making an immediate paper loss of £5.6m.
The remainder of the shares are being purchased by the government, which means that taxpayers have made an immediate paper loss of £2.4bn based on Thursday's closing share price.
"We regret that existing shareholders did not take up their pre-emptive rights but understand that market sentiment toward the banking sector made this uneconomic in the short term," said RBS Chief Executive Stephen Hester.
"There remain substantial uncertainties and challenges outside our control but for our part the job is underway."
RBS shareholders voted to take the government money at a meeting last week.
There will be strings attached, with the bank losing freedom in areas such as executive pay and dividend policy.
RBS also had to agree to return to "normal" lending practices, and last week it announced that it would guarantee overdraft rates and contracts for its business customers for at least a year.
The government's shares will be held by a company called UK Financial Investments Ltd, which is supposed to maximise value for taxpayers and prevent politicians making business decisions about banks.
Its chair will be Philip Hampton, chairman of Sainsbury's and former finance director of Lloyds TSB.
RBS is one of the many banks that has been hit by its exposure to debt based on US sub-prime loans.
It has also struggled with the collapse in inter-bank lending as the whole industry worried about which of their peers they could afford to lend to.
Critics say that RBS paid too much to buy ABN Amro last year.
It led a consortium that paid 71bn euros ($91bn; £61bn) for the Dutch bank in October 2007.