Royal Bank of Scotland (RBS) has announced losses for 2009 of £3.6bn ($5.5bn), after struggling with billions of pounds of bad loans.
Despite the losses, the bank is set to announce it will pay bonuses totalling £1.3bn to its staff.
But the bank's head, Stephen Hester, said it had lost money by not paying big bonuses to retain productive staff.
The UK taxpayer owns 84% of RBS after the government bailed out the bank at the end of 2008.
Chief executive Mr Hester told BBC Radio 4's Today programme: "We've had a small experiment in this respect... some of our best-performing people have been leaving in their thousands.
"The people who left us last year, I believe, would have increased our profits by up to £1bn beyond the ones that we've got."
However there has been some criticism of the bonuses paid.
Liberal Democrat treasury spokesman Vince Cable said that making hefty payouts to individual bankers was "like a football team paying their striker for scoring when they've just been relegated".
Meanwhile, shadow chancellor George Osborne said "unacceptable" pay levels throughout the sector must be tackled.
"The banking community needs to understand that the taxpayers were there for them a couple of years ago, because we had to keep the banking system going, but really it is unacceptable these very high levels of pay they get."
However RBS bonuses were approved by the Treasury, and Mr Osborne conceded he would not have blocked the payouts had he been in power.
Mr Hester has decided not to take his own bonus, which would have been £1.6m.
The company's £3.6bn loss was lower than the £5bn many experts were expecting and is well below the £24bn it lost in 2008.
However, the level of bad debts rose sharply to just short of £13.9bn, up from £7.4bn in 2008, although the bank says it thinks these have now peaked.
As well as the RBS chain of banks, the company's UK businesses include NatWest, Ulster and Coutts banks, and the insurance companies Churchill and Direct Line.
Mr Hester said he expected the bank to return to profit next year.
The banks have been through a torrid time since the credit crunch struck in 2007, an event sparked by the banks' own unwillingness to lend to each other after the major lending spree they had been on started to turn bad.
Added to that was RBS's unique heavy burden - its takeover of the Dutch bank ABN Amro in October 2007, just as the banking boom was about to turn to bust.
A consortium led by RBS paid 71bn euros (£49bn at the time) for ABN Amro in October 2007, but RBS then wrote down the value of the business by £17bn a year later.
The Bank of England governor, Mervyn King, said bank investors had been living in a "fool's paradise", with people's money being used for risky activities while they themselves thought they were taking no risks.
He told the cross-party Future of Banking Commission that the case for simple, utility banks was "irrefutable".
RBS is the second major UK bank to report 2009 results, after Barclays announced profits of £11.6bn last week. Lloyds Bank, which is also partly state-owned, will report its results on Friday.
Aside from bonuses, one other controversial topic for the banks has been their role in lending to business and home buyers.
RBS said that it was satisfied it was fulfilling both the letter and the spirit of its lending commitments, which were to make an additional £9bn available to the mortgage market and £16bn to businesses.
It said it had beaten its mortgage target, but had fallen short of its business lending target as many companies had been concentrating on reducing their debts and the recession meant that demand for loans had been weak.
RBS has shrunk massively in size over the year. In 2008 its assets stood at £2.1tn.
It has been running down a vast portion of its business - mainly bad loans - and its assets are now worth £1.5tn.
A bank spokeswoman said that was the equivalent of shedding an organisation the same size as the profitable US financial institution, Goldman Sachs.