More than two months after a deadly plane crash led to the worldwide grounding of the 737 Max, Boeing is facing mounting pressure from investors, airline customers and suppliers to get its flagship jet back into the air.
Boeing said the update has been tested on flight simulators and on 207 test flights, adding up to more than 360 hours of flight time.
"We are now providing additional information to address Federal Aviation Administration (FAA) requests that include additional detail on how pilots interact with the airplane controls and displays in different flight scenarios", the Boeing statement said.
On Wednesday, the House Committee on Transportation and Infrastructure questioned Federal Aviation Administration chief Dan Elwell and National Transportation Safety Board Chairman Robert Sumwalt about the planes after airlines throughout the world grounded the 737 Max in the wake of two crashes that killed almost 350 people in Indonesia and Ethiopia.
Boeing said that flight has not yet been scheduled.
Boeing Chairman and Chief Executive Officer Dennis Muilenburg in a statement cited "clear and steady progress" toward updating the MAX so that it will "be one of the safest airplanes ever to fly".
In both accidents, the automated Maneuvering Characteristics Augmentation System, or MCAS, pushed the planes' noses down while the pilots struggled to regain control. Between the two crashes, 346 people died.
Boeing's 737 MAX series planes are considered to be the most advanced and fuel-efficient single-aisle jets.
Southwest Airlines Boeing 737 Max 8 aircraft after being grounded in March.
This included customer conferences around the world, the first held in Amsterdam on May 7. "We don't know what training is like for Lion Air pilots or Ethiopian pilots".
Boeing's announcement about the software update followed the grilling of FAA acting administrator Dan Elwell by the US House Transportation Committee on Wednesday.
SilkAir's order of 31 Boeing 737 Max planes remains "intact", although the airline may not collect any of the planes in the near future.
Multiple investigations, including the initial crash investigation, are ongoing.
Boeing earlier triumphantly announced that it has implemented new failsafe features for the MCAS as well as new training manuals for pilots.
"I would call it the beta version", Lawrence said.
Elwell defended FAA's practice of designating employees of Boeing and other aerospace manufacturers to do some inspection work, saying it takes advantage of industry expertise, and "when done right, is indispensable to the health and safety of our system".
Aviation safety analyst Todd Curtis told the BBC that it would take a lot to convince the pilots and other flight crew members that the Boeing MAX aircraft was safe.