He entered the water several times, trying to cut Mr Solomon's harness, and continued to dive into the water to the point where he almost lost consciousness.
He had to be pulled out, and suffered from water in the lungs. He was taken to the ship's hospital for treatment.
Mr Solomon died in the accident.
Speaking at Government House in Auckland yesterday, where he was presented the New Zealand Bravery Medal, Chief Petty Officer Taylor was humble about the recognition.
"It's good, really good."
Talking about his actions, he said: "The last thing you think about at the time is yourself. One of your comrades is in trouble," he said. "Thinking about yourself just doesn't go through your mind."
His mother, Pat Taylor, said yesterday's ceremony - with its description of what her son had done that day - was the first time she had understood the magnitude of his actions.
"I didn't really think it was that eventful. But how they have described what happened, I kept looking over at [my husband] John, just amazed."