HSBC is closing scores of accounts in Jersey held by people who do not live on the island.
The move is part of a push by UK banks to check on the identity and addresses of thousands of their customers across the Channel Islands.
The review comes amid pressure on banks to ensure that offshore accounts are not being used to hide money from UK tax authority HMRC.
HSBC is writing to people who have accounts in Jersey but do not live there and advising them to open accounts closer to their home addresses.
The bank said: "While we cannot comment on individual cases, HSBC has implemented numerous standards designed to prevent its banking services being used to evade taxes or launder money, and we have exited clients who do not meet those standards or where we have concerns in relation to tax compliance."
In 2012 HMRC began an investigation into a data leak at HSBC in Jersey which led to allegations that British residents may have used accounts to launder money or evade taxes.
John Harris, director general of the Jersey Financial Services Commission, said: "We welcome any move banks take to manage risks and comply with international standards."
He added: "The number of bank accounts in Jersey has shrunk over the last couple of years, but this is only by around 1 or 2%.
"We have taken a strong stand against tax evasion."
The move comes after HSBC chief executive Stuart Gulliver last month apologised for the "unacceptable" tax-avoidance activities linked to the bank's Swiss arm in the mid-2000s.
The Swiss arm of the bank is charged with helping around 30,000 account holders comprising almost £78bn to hide these assets from the tax authorities in their home countries.
Almost 7,000 of these account holders are understood to be UK clients who held $21.7bn (£14.6bn).
Among those alleged to have been exposed as having accounts with the Swiss arm of HSBC are said to be politicians, sports stars and celebrities as well as criminals and traffickers.