Coutts, the exclusive private bank owned by Royal Bank of Scotland, got an 8.75 million pound fine from the financial regulator for failings in its anti-money laundering controls - its second in four months.
The latest fine follows a 6.3 million pound sanction in November for failings related to the sale of a fund product during the run-up to the 2008 financial crisis.
In October 2010, the Financial Services Authority (FSA) visited Coutts as part of its review into banks' management of high money-laundering risk situations.
Following that visit, the FSA's investigation identified that Coutts did not apply robust controls when starting relationships with high-risk customers and did not consistently apply an appropriate level of monitoring in that area.
Coutts' failings were significant, widespread and unacceptable. Its conduct fell well below the standards we expect and the size of the financial penalty demonstrates how seriously we view its failures, said Tracey McDermott, acting director of enforcement and financial crime, at the FSA.
Coutts, which was founded by Thomas Coutts in the 18th century, is one of Britain's best-known private banks. Its clients have included Queen Elizabeth II, sports people and pop stars.
The FSA said Coutts had started improving its anti-money laundering systems and had agreed to settle at an early stage with the regulator over the fine. If it had not done so, Coutts would have been fined 12.5 million pounds.
Last week, Coutts sold its Latin American, Caribbean and African private banking arms to Royal Bank of Canada, as part of its strategy to focus more on its key markets such as the UK, Switzerland, Russia, the Middle East and Asia.
(Reporting by Sudip Kar-Gupta; Editing by Myles Neligan and Erica Billingham)