A major airline industry union sued United Airlines in the Eastern District of New York this week, arguing that the airline breached its coronavirus-related contract with the federal government by reducing employees to part time.

United changed course on Wednesday, agreeing to make the part-time program voluntary, but it wasn't immediately clear how that move would affect the suit. Like other airlines, United has said it is suffering massive financial losses due to the pandemic.

The airline accepted $5 billion in April as part of the Coronavirus Aid, Relief, and Economic Security Act, and it agreed to "refrain from conducting involuntary layoffs or furloughs, or reducing pay rates and benefits," according to the complaint, which was filed Tuesday.

The employees represented by the International Association of Machinists and Aerospace Workers, AFL-CIO, also have a collective bargaining agreement that forbids United from replacing full-time shifts with part-time shifts, according to the complaint.

Nevertheless, on May 1, United informed the union that its workers would be reduced to part-time status, according to the complaint.

"United contended that this action was 'in full compliance with … the CARES Act,' apparently because, in its view, it was not reducing 'pay rates,'" John Grunert of Guerrieri, Bartos & Roma wrote in the complaint.

Grunert wrote that United had discussed the change to part-time status with union leaders before the company received its CARES Act funding, but it was described as something that might happen if funding were denied.

Even at that point, United conceded that it "did not have the authority to make this change without the union's consent," Grunert wrote.

United did not respond to a request for comment Thursday, but in a Wednesday memo to employees covered by CNBC and other news outlets, United Chief Operating Officer Greg Hart announced that the company would offer voluntary reduced work schedules instead of immediately reducing hours across the board.

"Given our continued need to cut costs across the entire company, this proposed program will only be successful if we have a high rate of participation. … Without a high level of participation, we will have no choice but to reconsider a mandatory reduction to 30 hours for our full-time employees," Hart wrote.

The employees who agree to work 30 hours will maintain full-time status, Hart added.

Grunert did not respond to a request for comment.

The case has been assigned to U.S. District Judge Rachel Kovner.

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