This disclosure relates to a system for preventing collisions with a terrain. The system includes a detecting means for detecting risks of collision with the terrain after a predetermined forecasting delay. The system further includes a determining means for determining, based on a trajectory followed by the aircraft, a possible limit point for success of the vertical terrain avoidance maneuver. The system further includes indication means for giving indications on azimuth clearance sections, around the direction in which the aircraft is moving, suitable for success of the vertical terrain avoidance maneuver. The system further includes means for estimating a free-travel distance in each azimuth clearance sector on a straight distancing trajectory with constant gradient and over a distance correspond to more than one minute of flight, the free-travel distance being free of potential conflicts with the terrain. The system further includes means for signaling azimuth clearance sections and free-travel distances.