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In a statement from manager David Higgins, Parker, the former WBO heavyweight world champion, paid tribute to Barry, saying the partnership had ended amicably.
The pair decided to part ways yesterday following Parker's unanimous points win over Junior Fa at Auckland's Spark Arena on Saturday.
"Without Kevin I wouldn't be where I am today," Parker said. "Together we made it to the very top. Kevin was with me every step of the way, guiding my progress inside and outside of the ring. So, it is with genuine sadness that I confirm our partnership has come to an end.
"But the time just feels right. It's fitting that we closed this chapter of my career with a win in front of a great home crowd in Auckland, and with bigger things just on the horizon.
"I know Kevin will always be in my corner."
Barry added: "I'm hugely proud to have played a part in New Zealand and Samoa crowning their first heavyweight world champion.
"It has been an amazing journey with Joseph and Team Parker. But all journeys must come to an end, and the time is right for myself and Joseph to go in our own directions.
"I have been in New Zealand for five months now, away from my family and my other fighters. I have three guys fighting for world titles this year and have responsibilities with them and a few new guys.
"It's not possible for me to stay in New Zealand any longer. For Joe, he has a wife and three young girls in New Zealand, and he wishes to spend more time here.
"I totally understand this and will always be in his corner and support him. We have always had a very close bond and I want nothing but the best for him. We have achieved so much together. It has been one heck of an amazing journey."
Barry's base in Las Vegas was a major barrier to the continuing partnership, but it's understood Parker was also keen for a change in direction due to several underwhelming performances over the last couple of years.
A former Olympic silver medalist, Barry guided David Tua to a heavyweight title shot against Lennox Lewis in 2000, and went one better with Parker by capturing the WBO heavyweight belt with Parker's victory over Andy Ruiz Jr in Auckland in 2016.
"With Kevin based in Las Vegas and Joseph keen to spend more time in New Zealand – and not to mention the restrictions on travel created by Covid-19 – this was a natural time for one of New Zealand's most successful sporting partnerships to come to a close," Higgins said.
"I'd personally like to pay tribute to Kevin. He worked tirelessly to make sure Joseph capitalised on his natural talent, and the results have been there for all to see. Kevin's place in history as New Zealand's finest boxing trainer is well and truly secure."
Parker and his team are in negotiations with Englishman Dereck Chisora for a fight in London on May 1. There will now be huge speculation about Parker's choice as his next trainer.