Although unnamed by police, it's thought 51-year-old tech entrepreneur Andrew Findlay was also aboard the 7.8m inflatable when it struck underwater rocks in large surf off Bondi Beach on Thursday morning.
Police found the body of Mr Klingender, 59, amid debris off Watsons Bay later that day. His death has shaken the art world, with many of his contemporaries lamenting the loss.
Mr Findlay remains unaccounted for but is presumed dead.
Marine Area Command Superintendent Joe McNulty told media on Saturday neither of the friends were wearing a life jacket when thrown into the sea.
"Those large swell have contributed to the loss of two good men," he said.
"Know your abilities, know your environment and the conditions."
Supt McNulty said a large search for the other man on board the vessel would be scaled down from Sunday.
Efforts to locate the missing man had been extensive.
"We threw the police divers at it and they searched 1000 metres of shoreline and underwater areas looking for the second person," he said.
Sup McNulty said police had vision of the two men fishing off Ben Buckler near Bondi and believed the boat they were in capsized in the five-metre swell when it struck a hidden rock ledge.
"This was a violent accident, a tragic accident we believe could have been avoided," he said.
"Both of them were not wearing life jackets. That's a terrible message to share with you today."
He said the men were trolling, a fishing method that involves trailing fishing lines behind a vessel. He said they were too close to the cliffs for the conditions.
Three police rescue boats were launched late on Thursday to conduct a search which extended five nautical miles, or almost nine kilometres out to sea.
Sup McNulty said the operation had spanned more than 20km on Saturday, from South head to Cape Solander near Botany Bay.
"We're at the conclusion now, we are wrapping the search up. The time-frame for survival for anyone in the water, taking into account the temperatures at the moment in July, have lapsed."
The four-tonne vessel the men were in is still lodged tight against the rocks under the cliffs at South Head, with police attempting to recover evidence from it.
Sup McNulty said police were appealing to anyone who was walking along the Gap in Watson's Bay on Thursday to contact them if they have further information.
