Lloyds Banking Group, owner of HBOS, is going to review the cases of customers affected by a fraud involving two ex-employees, who were jailed last week.
Six people, including the former HBOS bankers, were found guilty of a scam involving fraudulent loans.
The bank has been under pressure to pay compensation after it was accused of reacting too slowly to complaints from victims of the scheme.
The fraud took place before Lloyds Banking Group took ownership of HBOS.
"Customer cases will be considered afresh in light of all relevant evidence including new evidence that emerged during the trial," said a Lloyds statement.
"Since the investigation began in 2010, it was important that the group did not do or say anything that could subsequently prejudice the trial.
"The group deeply regrets that the criminal actions have caused such distress for a number of HBOS business customers."
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The statement explained that Lloyds would appoint an independent third party as part of the review and would agree the individual outcomes with it.
It added: "Lloyds Banking Group will contact all those customers they have identified as potentially affected by the criminal activities and provide redress if appropriate.
"Whilst this should result in all these customers being contacted proactively, any customer who believes they may have been affected can also raise concerns direct with LBG."
Some of the victims lost their companies, livelihoods and even their homes because of the scam.
Paul and Nikki Turner, from Cambridge, tried to report what was going on after their publishing company, Zenith, was run into the ground by the scammers.
They said they have had to fight hard for 10 years to have the fraud recognised.
'Needless third party'
Sources close to the investigation say the total value of the fraud may be close to £1bn.
"A number of us have already started actions against the bank and that will continue," said Joanne Dove, a member of HBOS Reading Action Group, who are former customers of the bank. Ms Dove lost millions through her nappy service firm as a result of the fraud.
"It would have been far better for the bank to admit a fraud had occurred, accept responsibility and then negotiate with the victims rather than appoint a needless third party consultant which will incur more expense, borne by LBG's shareholders and will possibly lead to extensive delays in agreeing compensation."