ANZ has started to refund $28.8 million to more than 390,000 accounts after the bank failed to disclose when some fee payment fees would apply.

ANZ discovered the problem, and reported the matter to the Australian Securities and Investments Commission as a "significant breach" of its financial services obligation, ASIC said today.

ASIC said the bank failed to clearly disclose when certain fees for periodical payments - which allow account holders to set and forget fixed amount payments - would apply.

Periodical payment fees are an alternative to direct debit arrangements, and allow customers to establish a regular payment to another account.

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Banks may charge a fee for this service, depending on the terms and conditions for the account.

ANZ has apologised to the affected customers, which includes 376,570 retail account holders and 17,230 business accounts holders.

The total amount that will be refunded, includes about $25.8 million of fees, with an additional $3 million in interest.

- AAP