IN THE light of falling interest rates and recent controversy surrounding offshore accounts, some banks might be reluctant to draw attention to their offshore sterling accounts. Yet despite the discouraging environment, Tyndall Bank International, a subsidiary of Tyndall Bank Plc, is offering high-interest accounts with visible results in Hong Kong. In the past year, the bank's Hong Kong depositors have grown by about 40 per cent and its profits have continued to rise. Recent events however suggest that Tyndall Bank - which set up operations in Hong Kong in 1989 - should perhaps be concerned that its four-year honeymoon may be nearing its end. Falling interest rates and increasing bank failures seem to suggest the bank has a few hurdles ahead. But Jupiter Tyndall Group Plc chairman John Duffield, on a visit to Hong Kong last week, said there was no reason for concern. Jupiter Tyndall Group is the parent company of Tyndall Bank. ''A growing number of Hong Kong people are using Tyndall's services,'' he said. Initiatives by Bank for International Settlements (BIS) - which is looking into a regulatory system for offshore banking centres - and the European Commission proposed directive, which would ensure European bank depositors were protected by their home bank in deposits throughout European branches, were litte more than points of interest for Tyndall. ''We are already regulated by every conceivable body,'' he said. And although the failure of the Bank of Commerce and Credit International (BCCI) and the publication of the Allen report on the Allied group's ties with the Cook Island's First South China Bank have cast the spotlight on offshore bank accounts, Mr Duffield said that no such controversy would affect Tyndall's offshore bank. ''As we are a non-lending bank, we would not have problems like BCCI anyway,'' he said. ''We are an absolutely pristine bank.'' Tyndall lends money on the inter-bank market, which makes it less vulnerable than banks involved in retail lending. Located on the Isle of Man, the bank's depositors are protected by the island's depositor-protection scheme. Subject to the Isle of Man's depositor protection scheme, Tyndall Bank International was forced to pay GBP250,000 million (about HK$2.83 million) each year for three years to compensate BCCI clients for their losses. But falling interest rates may turn out to be a problem. In October last year, for example, the UK base rate stood at eight per cent and by January of this year it had dropped to six per cent. The result has been that the bank's retail deposits are 1.8 per cent lower than they were in December, 1992. Fearing a further drop of 0.5 per cent, the bank recently introduced a controversial tiered interest rate structure to encourage clients to place higher amounts of money with the bank.