Around 160,000 customers of failed Icelandic bank Kaupthing Edge have been offered a new savings deal by ING Direct.
The Dutch savings bank said it had now successfully integrated all of the Kaupthing Edge accounts into its system.
The group took on £2.5bn worth of deposits from Kaupthing Edge in October last year in a move arranged by the Treasury to protect UK savers amid concerns about the Icelandic banking sector.
Following their integration into ING's system, the former Kaupthing Edge customers have been moved to a new rate, which currently pays 2 per cent and is guaranteed to be at least 0.3 per cent above the Bank of England base rate until 2012.
But customers are being given the option of moving to a different rate of 4 per cent, which includes a bonus of 2.02 per cent which is paid for six months.
After this the rate reverts to ING's standard rate, which does not include a guarantee.
Former Kaupthing Edge customers were previously on a rate of 3.55 per cent with ING, after the group did not pass on any of either January or February's base rate reduction while it integrated the savers into its system.
People have until 9 March to opt for the 4 per cent, while they remain free to withdraw their money and move it elsewhere if they want to.
Around 22,000 customers of Heritable Bank, which was part of Icelandic bank Landsbanki, were also moved to ING, but they have not yet been integrated into the group's systems.
Kevin Mountford, head of banking at moneysupermarket.com, said: "The majority of personal savers with failed Icelandic banks survived a big scare last year. Dutch giant ING came to the rescue of Kaupthing customers but, after enjoying some market-leading rates with Kaupthing, these savers are coming back to earth with a bump.
"While many experts sniff at the use of bonuses as a way of attracting savers and headlines, 4 per cent is not bad at all in today's market, even with a bonus.
"It's likely that bonus accounts will actually provide a further stimulus to the savings market by encouraging savers to change accounts more regularly, thereby increasing competition, at least in the short-term."
But he stressed that it was important that savers who took out a bonus account made a note of when the introductory offer period ended so that they could review their options.