Washington (CNN Business) An anonymous pilot is suing Boeing, alleging the company "demonstrated reckless indifference and conscious disregard for the flying public" in its development of the 737 Max.

The suit also accuses the Federal Aviation Administration of joining Boeing "in an unprecedented cover-up of the known design flaws of the Max, which predictably resulted in the crashes of two Max aircraft and subsequent grounding of all Max aircraft worldwide."

The FAA is not named as a defendant in the lawsuit, but aviation attorney Joseph Wheeler, one of the lawyers representing the unnamed plaintiff, told CNN he has begun the administrative procedure that "is a necessary procedural precondition to filing suit against the FAA."

Both Boeing spokesman Peter Pedraza and an FAA spokesman declined to comment on the matter. The lawsuit was filed on Friday in Cook County, Illinois, which is home to Boeing's Chicago headquarters.

The Max planes that are the latest variants of Boeing's workhorse 737 series were grounded in March after two crashes in less than six months that together killed 346 people. The investigations are ongoing, but preliminary reports showed similarities between the two crashes, and Boeing is overhauling the new computerized stabilization system known as MCAS.

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