A system indicating to a pilot that an aircraft has passed the limit-point of success of a standard vertical avoidance maneuver is disclosed. To determine the limit-point, the system monitors a penetration of a model of the terrain being flown over into a first protection volume linked to the aircraft and configured so as to model a standard vertical avoidance maneuver path executed without delay. To determine disengagement azimuth sectors, the system monitors the penetrations of the model of the terrain being flown over into a second protection volume with large azimuth aperture, linked to the aircraft and configured so as to contain the limit-point protection volume and, for the various azimuths covered, paths of a composite maneuver beginning with change-of-heading maneuvers with which to reach the azimuth concerned and continuing with the standard terrain vertical avoidance maneuver.