A method is provided for assisting in rejoining a vertical descent trajectory that an aircraft is assumed to have to follow, using a flight management system FMS embedded onboard the aircraft, and includes the following steps: calculation of a vertical deviation VDEV, in the vertical plane, between the aircraft and the vertical descent trajectory, and comparison between the vertical deviation VDEV and a predetermined deviation threshold SVDEV; when the vertical deviation VDEV reaches the deviation threshold SVDEV, a step during which the activation of an optimized mode for catching up on the vertical descent trajectory is authorized; if the optimized mode for catching up on the vertical descent trajectory is activated, piloting of the aircraft by the flight management system FMS in optimized catch-up mode, that is to say at minimum thrust with a target rejoining speed in level VCRP and a target rejoining speed in downward trajectory, the target rejoining speed in level VCRP being equal to the maximum L/D ratio speed of the aircraft uprated by a first value V1 of between 5 and 15 knots, and the target rejoining speed in downward trajectory VCRD being equal to the maximum operating speed VMO with which the aircraft is allowed to fly downrated by a second value V2 of between 3 and 10 knots, a knot being equal to 0.514 ms−1.