A new flaw that could result in the plane's nose pitching downwards has been found on the Boeing 737 Max, the airline manufacturer said. It is almost certain to further delay the plane's return to the skies after two deadly crashes.

The software problem in the plane’s computer system was discovered by Federal Aviation Administration (FAA) test pilots updated Max software in a flight simulator, Boeing said.

The flaw could result in the plane's nose pitching down, two people familiar with the matter told the Associated Press news agency. Both spoke on condition of anonymity to discuss aspects of the review process that are not public.

In both Max crashes, the plane's flight-control software pushed the nose down based on faulty readings from one sensor.

"Boeing agrees with the FAA's decision and request, and is working on the required software to address the FAA's request," the firm said in a statement.

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It is thought that fixing the issue might be accomplished through software changes or by replacing a microprocessor in the plane's flight-control system. The latest setback could delay the plane's return to service by an extra one to three months.

Boeing has been working to get its best-selling aeroplane back in the air following a worldwide grounding in March in the wake of two deadly crashes within five months.

Last month, FAA representatives told members of the aviation industry that approval of the 737 Max jets could happen as early as late June.

Boeing has been working on an upgrade for the stall-prevention system known as MCAS since a Lion Air crash in Indonesia in October, after the software repeatedly pushed the nose down.

A second deadly crash in March, involving and Ethiopian Airlines jet also involved MCAS.

In total, 346 people died in both crashes.

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“On the most recent issue, the FAA’s process is designed to discover and highlight potential risks. The FAA recently found a potential risk that Boeing must mitigate,” the FAA said in a statement. “The FAA will lift the aircraft’s prohibition order when we deem it is safe to do so.”

It added that it was continuing ”to evaluate Boeing’s software modification to the MCAS and we are still developing necessary training requirements."

It added: "We also are responding to recommendations received from the Technical Advisory Board. The TAB is an independent review panel we have asked to review our work regarding 737 Max return to service.”