At a press conference, bank officials said that Hisco's departure was linked to the use of chauffeur-driven cars and storage, reports Xinhua news agency.
"Hisco's departure follows ongoing health issues as well as board concern about the characterization of certain transactions following an internal review of personal expenses.
"While Hisco does not accept all of the concerns raised by the board, he accepts accountability given his leadership position and agrees the characterization of the expenses falls short of the standards required," the bank said in a statement.
ANZ New Zealand chairman and former New Zealand Prime Minister John Key said Hisco had forfeited his right to $4.16 million in equity in the bank.
Key did not think there were any systemic problems in the senior leadership in the bank, and said the it had been reviewing the anomalies in expenses for three months.
Antonia Watson was appointed as acting CEO of ANZ New Zealand, following the departure of Hisco, who had been the CEO since 2010.
ANZ suffered a couple of regulatory blows last month with the Reserve Bank of New Zealand forcing it to hold more capital against housing and farm lending from June 30 and to use the standardized model for calculating its operational risk capital rather than its own internal model.
( With inputs from IANS )