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Boeing 737 Max 8 planes will be back in the air 'very soon,' its CEO says

You could be onboard one of Boeing's most notorious planes by the end of the year.

The aircraft manufacturer has started the process to regain Federal Aviation Administration certification for its 737 Max 8 jets, Boeing CEO Dennis Muilenburg told CNBC on Monday. Boeing recently issued a software update for the aircraft's flawed anti-stall system, and now Muilenburg says it should be back in use for commercial airlines by the end of the year.

737 Max 8 planes were grounded around the world in March after two of them crashed, killing 346 people total. A series of reports later tied the crashes to other reported issues with the model's anti-stall mechanism and suggested Boeing was aware of the flawed technology but didn't move quickly to fix it.

The FAA now has to recertify the aircraft before it can get back in the air. Boeing has scheduled simulated flights with the FAA for this week, Muilenburg said, and added that "we hope to schedule the certification flight very soon." The FAA would then decide if the Max 8 planes are skyworthy. So far in the regulatory process, the FAA found that more than 300 Boeing 737 jets had faulty wing parts that need to be replaced before they can fly again.

Watch Muilenburg's whole CNBC interview below. Kathryn Krawczyk