A device for avoiding a potential conflict detected in a predetermined trajectory prediction horizon between a first trajectory of a first ship or aircraft and a second trajectory of a second ship or aircraft is disclosed. Each trajectory includes a plurality of segments formed between multiple navigation points. The device includes a determination unit for determining at least one lateral peripheral envelope of the first trajectory, a division unit for dividing the lateral peripheral envelope into a plurality of juxtaposed sections arranged longitudinally the ones after the others and delimited by transition lines marking the change between sections, each transition line cutting, at a first point of intersection, a segment of the first trajectory and, at a second point of intersection, and an edge of the lateral peripheral envelope, a discretisation unit, and a computing unit.