Air Traffic Management (ATM) of the future allows for the possibility of free flight, in which aircraft choose their own optimal routes, altitudes, and velocities, The safe resolution of trajectory conflicts between aircraft is necessary to the success of such a distributed control system, In this paper, we present a method to synthesize provably safe conflict resolution maneuvers. The method models the aircraft and the maneuver as a hybrid control system and calculates the maximal set of safe initial conditions for each aircraft so that separation is assured in the presence of uncertainties in the actions of the other aircraft, Examples of maneuvers using both speed and heading changes are worked out in detail.