WASHINGTON/SEATTLE (Reuters) - Boeing Co plans further changes to the software architecture of the 737 MAX flight-control system to address a flaw discovered after a test in June, two people briefed on the matter said late on Thursday.

The redesign, first reported by the Seattle Times, involves using and receiving input from both flight control computers rather than one.

The move comes in response to an effort to address a problem discovered in June during a Federal Aviation Administration(FAA) simulator test.

This is on top of earlier announced changes to take input from both angle-of-attack sensors in the MCAS anti-stall system linked to two deadly crashes that led to a global grounding of the plane.

Boeing still hopes to complete the software redesign by the end of September to submit to the FAA for approval, the sources said.

For decades, 737 models have used only one of the flight control computers for each flight, with the system switching to the other computer on the following flight, according to people familiar with the plane’s design.

The FAA said in June that it had identified a new risk that would need to be addressed before the plane could be ungrounded.

Under a scenario where a specific fault in a microprocessor caused an uncommanded movement of the plane’s horizontal tail, it took pilots too long to recognize a loss of control known as runaway stabilizer, a Boeing official said at the time.

Boeing Chief Executive Dennis Muilenburg told analysts last month that he was confident the 737 MAX would be back in service as early as October after a certification flight in “the September time frame”

Southwest Airlines and Air Canada, however, have taken the 737 MAX off their schedules until January.

The FAA declined to comment on the Seattle Times report. Boeing did not respond immediately to a request for comment.