The Treasury is to sell off a stake of up to 5% in Lloyds Banking Group over the next six months raising about £3 billion.
Taxpayers still own 25% of the group, which also includes Halifax, after its £20 billion rescue during the financial crisis.
A plan launched today by Chancellor George Osborne will see up to a fifth of this chunk sold off through City firm Morgan Stanley.
But it is possible that the sale, which may begin within days, does not dispose of as much as a 5% stake, because the Treasury has instructed that no shares can be sold below the average price the previous government paid for them, of 73.6p.
Shares fell about from nearly 77p to just over 75p today.
The Government has chosen to sell the stock over time "in an orderly and measured way" rather than through large tranches as has been done previously.
Disposing of the shares in bigger chunks normally involves offering a significant discount to attract large-scale investors but the latest plan appears to be an attempt to avoid this so as to gain better taxpayer value.
The Government has previously raised £7.4 billion after reducing its stake in Lloyds from around 40% to just under 25%.
"The trading plan I'm initiating today is made possible by our long-term economic plan which is delivering a more secure and resilient economy. It is another step in reducing our national debt and in getting taxpayers' money back."
The announcement comes a day after Lloyds scraped through a Bank of England stress test which suggested it was "susceptible to a severe economic downturn" though its most recent actions to shore up the business left it on a firmer footing.
Lloyds was not ordered to take any further action, prompting analysts to conclude it paved the way for the group to re-start dividend payments in spring next year - making the shares more attractive as the Government seeks to sell them.
The new trading plan was launched following advice from UK Financial Investments (UKFI), which controls the state's stakes in bailed-out banks including Lloyds and Royal Bank of Scotland.
UKFI said it will mean no more than 15% of the "aggregate trading volume" of the group to be sold over the duration of the period - which it is possible may not begin until the new year and will end by June 30.
This equates to about just under £3 billion worth of Lloyds shares, or just over 5% of the group.
A pre-election sale of shares in Lloyds to ordinary members of the public was ruled out earlier this year by the Chancellor.
The first sale by the Government of its stake in the bank back to the private sector saw a 6% chunk disposed of in September 2013.
But a National Audit Office report found that it left taxpayers nursing a £230 million loss, despite the offer price of 75p - more than the Government paid for the shares - because of the cost of borrowing money to finance the 2009 rescue of the group.
Keith Bowman, equity analyst at Hargreaves Lansdown stockbrokers, said: "The Government's determination to recoup the taxpayer's bailout investment is being further underlined.
"The announcement comes just a day after Lloyds passed the Bank of England's stress tests and ahead of a General Election, for which the economy and the public finances will prove a key battleground.
"In addition, the announcement may also further disappoint private investors, with opportunity for them to buy shares in the part taxpayer owned bank again being omitted.
"In all, Lloyds continues to benefit from a recovering UK economy, the trajectory of which remains a major influence over the Government's own sale process."
A Lloyds spokesman said: "We are pleased that the Government has announced its intention to sell part of its remaining shareholding in Lloyds Banking Group and allow taxpayers to get more of their money back.
"This reflects the hard work undertaken over the last three years to make Lloyds a safe and profitable bank that is focused on supporting the UK economy."
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