A method and a device for the filtering of alerts originating from a collision detection system of an aircraft makes it possible, by proposing a novel condition for alert disabling, to avoid an abnormal drop of an aircraft in the case of a CFIT (controlled flight into terrain) by authorizing the output of the alert when this novel condition is not complied with. This novel condition relies on a method for thresholding the angle of approach of the aircraft (FPA for flight path angle) as a function of the altitude of the aircraft with respect to the runway and of the angle of approach specified for each runway and which is recovered via the terrain database.