"From additional testing and serology analysis, we have determined there is no link to the Christchurch returnee group," the Ministry of Health said in a statement.
"Any infection would have occurred overseas prior to the person returning to New Zealand earlier this month and they are no longer infectious."
"As we have previously said about historical cases, we know that some people can return a positive PCR test long after they have recovered from the illness and are no longer infectious."
All 86 passengers on the flight have now been tested, except one, a young child. All have been negative apart from the three previously reported cases and the one case confirmed today.
That testing regime was started after a man in his 40s and flew home to Auckland on a chartered flight. He had returned to New Zealand from India on September 11 and spent 14 days in managed isolation in Christchurch.
He then tested positive, and is believed to have contracted Covid-19 after a rare 21-day incubation period.
Two people who were on the same chartered flight from Christchurch also tested positive, along with a household contact. The three infected people went to Taupō (before discovering they were infected) and met with a group of 18 others last weekend.
Bloomfield said that was "not ideal" because the maximum gathering size for Aucklanders was still 10 at the time. But the families had carefully used the contact tracer app which had made it easier for public health officials to track their movements easily.
Meanwhile, the ministry said today there were 32 people isolating in the Auckland quarantine facility from the community, including 15 people who have tested positive and their household contacts.
There are now two people in hospital with Covid-19, down one from yesterday. Both patients are in isolation on a general ward.
It is the first weekend since Auckland moved to alert level 2 and the rest of the country to level 1.
Aucklanders leaving the city for the school holidays have been urged to take their alert level restrictions with them.
The exodus of Aucklanders comes as scientists say the newest Covid cluster has the potential to be very serious.
Having stemmed from a rare Covid case which emerged after the person had left managed isolation, it could also force officials to rethink how long people are kept in isolation, one expert said.
Bloomfield said yesterday Aucklanders should still behave as if they were in alert level 2 even if they were outside the city.
"Even as we go into the school holidays … a reminder to Aucklanders – great they will be travelling around the country, and it's good we're in a position they can do that - just to be mindful," he told RNZ.
There were two new Covid cases confirmed yesterday, one a traveller from overseas and the other in the community - a young woman who was already in isolation.
