Ulster Bank has a "worst case scenario" DIRT liability over 12 years of £900,000, the inquiry was told yesterday, although the figure has not been finalised.
Mr Oliver Lynas, head of group audit, said when he took responsibility for tax compliance in the Republic in late 1993 or 1994, "the compliance was very poor".
He added that, "on a worst case scenario", DIRT liability on non-resident accounts without proper declarations was estimated at £900,000, a figure which did not include interest or penalties, but which had not been agreed within the group.
Mr Ronnie Kells, Ulster Bank's former chief executive, said DIRT compliance became an important issue to him around 1991 because progress had not been made in improving the standard of compliance in the branches.
An annual review was undertaken which led to "a definite improvement".
Asked about the problem of people living near Border areas opening up non-resident accounts in different jurisdictions, he said it "was not something that was a large-scale thing".
Mr Martin Wilson, group chief executive, said that despite the bank's efforts, it had not always maintained the standard of documentary evidence "which I would wish to see".