The procedure is known as a "domino" heart transplant where the heart of one patient undergoing heart-lung transplantation is donated to another recipient.
Transplanting heart and lungs together ensured there would be enough pressure generated by the heart to exactly match the lungs and the instant blood supply aids the fast healing of the windpipe.
With a shortage of available donor organs, Yacoub did not believe that a potentially functioning heart should be sent to the pathology department.
The Dutchman who received Burnett's heart would later send her a postcard expressing his gratitude.
"Now we will know again what it is like to make our own toast and coffee in the morning," he wrote.
He wanted to meet Burnett and when she was interviewed by Lin Ferguson of the Whanganui Chronicle in 2013, she expressed regret that it did not happen.
"At the time I just couldn't," she said.
There were not many regrets for Burnett as she regained her strength, returned to work and watched her daughters grow.
She also returned to playing hockey and tennis and twice competed in the World Transplant Games in Britain and Canada, winning a bronze medal in shot put.
In 1992, she told the Chronicle's Colin Rowatt that she was celebrating the fifth anniversary of her "rebirth".
"I've been bloody lucky I guess," she said. "But I reckon I'm going to be around for a few more years yet."
When Rowatt asked how she was, her response was emphatic.
"Me!" she exclaimed. "What do you want to know that for? You can see ... I'm all right."
Two years later, the anti-rejection drugs she was taking caused her kidneys to fail and she would once again count herself "lucky" when a suitable donor was found and she would once again recover from a transplant operation performed at Wellington Hospital.
Rangitīkei mayor Andy Watson said he hadn't seen a lot of Burnett in recent years but recalls her steely determination.
"She had to be very disciplined as well," he said.
"Consistently sticking to her medication regime and always adhering to the advice of medical professionals can't have been easy either."
In 2017 Burnett celebrated the 30th anniversary of her heart and lung transplant at Shed 5 restaurant on Wellington's waterfront with her family, friends, doctors and fundraisers who all helped her to reach her incredible milestone.
Not only did she get to see daughters Cherie and Melissa grow up but became a grandmother to Daniella, Connor, and Heath.
Burnett requested a private farewell which has taken place.
Well-wishers can leave messages for her family at legacy.com