The present invention relates to a construction method of a joint flight path to a mobile point including the step of acquiring a first state vector defining the position of the aircraft at the moment t0, acquiring a second state vector defining the position of the mobile point at each moment t after the moment t0. The method further includes determining, for each position of the mobile point, an elementary join flight path of this position of the mobile point from the position of the aircraft defined by the first state vector at the moment t0 with a capture time Tt corresponding to the time of flight of the aircraft on this flight path. The method also includes determining the flight path such that its capture time Tt is substantially equal to the time elapsed between the moment t associated with this trajectory and the moment t0.