Lloyds TSB has said that it will now pay immediate interest on cheques before they are cleared.
Quicker interest for Lloyds TSB customers
The bank says it is the first in the UK to do this, in response to discontent among customers who think banks take too long to clear cheques.
But it is not giving customers instant access to the money being deposited.
The Office of Fair Trading will publish a report this summer into ways the banks can speed up the underlying three-day cheque clearing system.
A survey of 8,000 High Street bank customers has revealed what critics have always claimed - that customers are fed up with banks taking their cheques, but not crediting them with the money or the interest until after the three-day cycle for cheque clearing has been completed.
Lloyds TSB says its move will benefit customers depositing cheques worth up to £1,000 each.
The change will apply regardless of whether or not the customers are in the black or are running an overdraft.
Changes on the way
Although the use of cheques has been declining rapidly in recent years, in the face of the more popular debit cards, the bank's customers last year deposited 55 million of them, worth £32bn.
Last year the banking industry body, the Association for Payment Clearing Services (APACS) reported that the number of cheques written in the UK halved between 1990 and 2004.
Of these only 19% were used in shops while 13% were used to settle credit card bills. A further 19% were for regular bills such as utilities and another 17% were paid to businesses, for example plumbers.
The Halifax bank has already predicted that on current trends cheques will become extinct within 20 years.
The banking industry has already agreed that by next year transfers of money which are triggered by instructions over the phone or internet will take place on the same day.