Two months after a pair of catastrophic crashes led to the grounding of Boeing’s 737 MAX jets worldwide, the company says it has finished work on a software update aimed at heading off future safety issues with an automatic flight control system.

Boeing announced the completion of software development today, and said it’s working with the Federal Aviation Administration to finish the process of getting the plane certified for its return to flight.

The update affects the 737 MAX’s Maneuvering Characteristics Augmentation System, or MCAS, which Boeing added to the jet to make the cockpit controls work as they did on previous-generation 737 planes.

After the fatal crashes in Indonesia last October and in Ethiopia this March, investigators tentatively concluded that the MCAS system repeatedly forced both planes into nose dives, due to spurious data that the system was receiving from a single angle-of-attack sensor mounted on each plane’s exterior. In each case, the pilots were unable to wrest back manual control.

The software update is designed to disengage MCAS if readings from the two angle-of-attack sensors substantially disagree, and it also sets tighter limits on the automatic controls.

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. Now the company is responding to FAA requests for more details on how pilots interact with the airplane controls and displays in different flight scenarios. Once those requests are addressed, Boeing will work with the FAA to schedule a final certification test flight and submit final certification documentation.

“With safety as our clear priority, we have completed all of the engineering test flights for the software update and are preparing for the final certification flight. We’re committed to providing the FAA and global regulators all the information they need, and to getting it right,” Boeing CEO Dennis Muilenburg said in a news release.

“We’re making clear and steady progress and are confident that the 737 MAX with updated MCAS software will be one of the safest airplanes ever to fly,” Muilenburg said. “The accidents have only intensified our commitment to our values, including safety, quality and integrity, because we know lives depend on what we do.”

Boeing has also developed enhanced training and education materials that are being reviewed by the FAA as well as Boeing’s airline customers and other regulators around the world. On May 23, the FAA is due to convene a meeting in Texas to review the preparations for a return to service, and Boeing indicated that similar conferences would be conducted in other locales.

Analysts say 737 MAX planes could be back in operation by late summer if all goes well. But the investigations, hearings and court cases spawned by the crashes could well go on much longer.