Australian-owned bank BNZ will drop penalty fees on all overdrawn personal and business accounts from the beginning of September.
BNZ says it will stop charging honour fees, dishonour fees and unpaid bill fees on transaction and savings accounts, which range between $5 and $35 every time an account goes into the red.
The bank says in many cases a customer's account is overdrawn due to some payments coming out early or their salary going in a day late, and it generates a large number of complaints.
BNZ is a subsidiary of National Australia Bank (NAB), which is axing its $A30 overdrawn charge from all personal savings accounts and personal transaction accounts from 1 October.
The move is also aimed at appeasing customers, with NAB receiving more complaints about the fees than anything else.
An overdrawn fee is paid when withdrawals from a bank account exceed the available balance, giving the account a negative balance.
Australia's other major banks are reviewing their charges on overdrawn accounts in a bid to stay competitive after NAB abolished its fee.
The Commonwealth Bank of Australia said on Wednesday it was about to announce a significant reduction in fees in this area.
An ANZ spokeswoman said the bank was aware of customer concern about fees for overdrawn accounts.
Westpac also said it had been reviewing its fee structure for some time. St George Bank, which trades under Westpac Banking Corporation after merging last year, said its fees "were under review".