The search for Malaysia Airlines flight MH370 by a private US firm will end next Tuesday and there will be no more extensions, Malaysia's transport minister has announced.

Houston-based group Ocean Infinity has been searching for the aircraft that disappeared en route from Kuala Lumpur to Beijing on March 8, 2014, with 239 people on board in one of the world's greatest aviation mysteries.

Malaysia's transport minister Anthony Loke today announced the company had been granted its final extension to May 29, news.com.au reports.

Asked if that meant no more extensions, he said: "Yes".

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The Ocean Infinity search comes after Australia, China and Malaysia ended a fruitless A$200 million search across a 120,000 square-kilometre area in the Indian Ocean last year, despite investigators calling for the target area to be extended 25,000 square kilometres north.

The announcement follows the Australian Transport Safety Bureau breaking its silence on claims it was complicit in a mass murder cover up.

Officials Greg Hood and Peter Foley have defended their search for the Malaysian Airlines flight, rejecting claims the pilot performed a controlled ditching.

Foley said claims the ATSB had ignored a theory in which the pilot flew the plane to the end were wrong.

"There's no earthly reason why someone in control of an aircraft would exhaust its fuel and then attempt to glide it when they have the option of ditching," Foley said.

"The aircraft was probably descending in an uncontrolled manner."

But several other aviation experts and investigators have suggested otherwise, saying Captain Zaharie Ahmad Shah hijacked his own plane, depressurised it to kill everyone else on board while using the pilot's long oxygen supply and continued to fly it before ditching it.

Peter Foley said they deeply regretted not being able to find the plane. Photo / news.com.au
Peter Foley said they deeply regretted not being able to find the plane. Photo / news.com.au

If the pilot was still in control, that means he could have flown the aircraft further than if it was on autopilot. This includes gliding it when fuel supplies ran out.

Their theories change the flight path and where the current search team should be looking.

Foley told a Senate estimates hearing on Tuesday that even if Zaharie had changed the cabin pressure he would have knocked himself out in the process.

"Most of the people out there are speculating about a long period of depressurisation after the transponder went off," he said.

"What they fail to understand is that while you don an oxygen mask and prevent the worst of the hypoxia situation, you are flying an aircraft at 40,000 feet.

"You are taking an aircraft from sea level to Mt Kosciuszko in 20 minutes, then you are taking it, over the course of a couple of minutes, to the height of Mt Everest plus 1000 feet. You'll get decompression sickness too."

He said that theory relied on the pilot fighting the effects of decompression sickness for an hour, which was unlikely given the pilot was 53 and overweight.

Mr Foley said they deeply regretted not being able to find the plane and the 239 people on board and agreed with comments it "torments your soul".

A recent book by Canadian Larry Vance, a former commercial pilot who worked as a senior air-crash investigator with Canada's Transportation Safety Board, has cast doubt on the ATSB's findings in his book MH370 Mystery Solved.

Vance presents evidence contradicting the bureau's conclusion MH370 likely entered an out-of-control high-speed descent and crashed into the ocean.

But Foley told the hearing the last transmission from the plane was incomplete and probably triggered by fuel exhaustion.

One of the plane's flaps found off the coast of Tanzania in July 2015 was a crucial piece of evidence, Foley said.

He said that showed the flaps weren't deployed at the end of the flight, meaning the aircraft was uncontrolled or poorly controlled.

"We have quite a lot of evidence to support no control at the end," he said.

Foley said the ATSB had also spoken to other experts including Boeing 777 instructor Simon Hardy who said in a 60 Minutes program the pilot "deliberately" avoided detection while flying.

"Some of Simon's initial area where he was postulating it was controlled to the end, but not a ditching — we actually searched. We went a long way to the east in that search — 42 miles.

"We haven't ever ruled out someone intervening at the end. It's unlikely."