Directors of Southwest Airlines Co. say the CEO is staying put even if union leaders want to get rid of him.

Late Friday, the airline released a letter in which directors said they were unanimous in supporting CEO Gary Kelly.

The board cited a long list of achievements since Kelly became CEO in 2004. It said the unions' call for his removal was without merit and reckless, and there was no guarantee that unions would like new management any better.

This week four union leaders, frustrated over the lack of agreement on new labor contracts, had called for Kelly and Chief Operating Officer Mike Van de Ven to be replaced after a technology outage caused the airline to cancel more than 2,000 flights.