Mr Puna says anyone leaving the Cook Islands will now only have to check in and follow the normal security checks before departure.
However, arrival cards will still need to be completed.
Meanwhile, Mr Puna arrives in New Zealand today for a week of events marking the country's 50th anniversary of self government.
It follows gala events on Rarotonga last week.
The New Zealand Prime Minister John Key says the anniversary is a significant occasion for both our countries and he says New Zealand is returning the hospitality it receives during last week's events with an official lunch.
Mr Puna will also attend a Cook Islands community celebration and a breakfast with members of the New Zealand-Pacific Parliamentary Friendship group.