Commonwealth Bank of Australia (ASX:CBA) unit ASB Bank has been imposed a final penalty of NZ$2.1 million by the High Court of New Zealand under a Financial Markets Authority lawsuit, according to a Thursday statement by the regulator.

The regulator said ASB admitted making false and/or misleading representations that resulted in financial harm to customers, including failure to correctly apply multi-policy discounts on ASB-branded insurance products and failure to apply fee exemptions for eligible FastNet Business customers.

More than 25,000 customers were refunded around NZ$4.7 million by ASB as a result of the issues, the statement added.

Financial Markets Authority Head of Enforcement Margot Gatland said the penalty reflects the seriousness of ASB's systems failures.

"Customers are entitled to rely on their bank to apply discounts and fee exemptions accurately. ASB failed to detect and address these issues over many years," Gatland said.

Commonwealth Bank's shares were up past 1% in recent Thursday trade.