Bank of Ireland has announced plans to raise €3.4bn that will see the Irish government's stake in the bank rise to 36%.
The Republic's biggest bank said it would raise up to €1.9 bn in a rights issue for private investors and another â‚¬500m in a share placing with institutional investors.
It plans to raise the remaining €1bn by converting some of the so-called preference shares held by the Government into ordinary shares.
Under the terms of the deal the Government's stake in Bank of Ireland would rise from 16% to 36%.
However, after the capital raising exercise Bank of Ireland will be the only Irish bank which was rescued by the Irish Government two years ago that will not be majority State-owned.
Bank of Ireland, along with Allied Irish Banks and Anglo Irish Bank, has recently transferred the first tranche of problem loans linked to the collapse of the property market into the Government's "bad bank", the National Asset Management Agency (NAMA).
Matthew Elderfield, the Republic's financial regulator, told Bank of Ireland last month it needed to raise €2.7bn in capital by the end of the year to meet new requirements on minimum capital for banks.
The Republic's Finance Minister Brian Lenihan said the transaction was good news for the Irish economy, its taxpayers and Bank of Ireland's shareholders and investors.
In a separate interim management statement to the stock markets, the bank signalled that the market remains difficult.
"Trading conditions in our core markets in Ireland and the UK in the first quarter of our 2010 financial year remain challenging though economic conditions have recently shown some signs of stabilisation after the substantial fall in economic output from early in 2008," it said.
"The challenging economic conditions, unemployment and weak consumer sentiment continue to impact the loan impairment charge as expected. We continue to believe that loan losses on our non-NAMA-bound loan portfolios have peaked with the impairment charge progressively reducing as previously guided."
The Bank of Ireland expects to transfer €12bn of toxic loans into NAMA.