FILE PHOTO - The logo of the National Australia Bank is displayed outside their headquarters building in central Sydney, Australia August 4, 2017. REUTERS/David Gray

SYDNEY (Reuters) - The head of Australia’s sovereign wealth fund criticized National Australia Bank Ltd on Monday for the double resignation of its CEO and chairman after a misconduct inquiry, saying it was “not good practice” for both to go at once.

The comments from Future Fund Chairman and former federal treasurer Peter Costello put Australia’s big banks on notice that investors are paying close attention to governance issues in the wake of the year-long inquiry into financial-sector misconduct. The Future Fund is Australia’s biggest investor with A$8.5 billion ($6 billion) in shares.

“If the NAB was managing itself well ... the chairman would go first and then a new chairman or chairwoman would appoint the CEO,” Costello told reporters on a media call, referring to the resignations last week of NAB Chief Executive Andrew Thorburn and Chairman Ken Henry.

“I don’t think it’s good practice to have an outgoing chairman to appoint the new CEO (because) the first thing any CEO coming into the NAB is going to want to know is who’s the chairman? I don’t know if they’ve handled the transition well.”

Thorburn and Henry resigned on Thursday days after being singled out for strong criticism in the final report of the Royal Commission inquiry, which found widespread greed and wrongdoing in the financial sector.

The CEO would leave this month but Henry would stay until a replacement was found, the bank said.

Henry said last week he needed to stay to “ensure an orderly succession of the CEO and also to ensure appropriate board renewal”. Asked about Costello’s comments, an NAB representative had no further comment.

Costello also said the Royal Commission showed that regulators had to “do a lot more” to clean up the financial system.

Costello gave his remarks as the A$147 billion sovereign fund reported a 5.8 percent return for the year to end-December, below its 6.6 percent target but better than the average 0.6 percent return for managed funds following market turmoil in late 2018.