Abstract: In order to pilot an aerodyne between two geographical positions associated with a transition route constraint, the method according to the invention comprises the application to each of these positions of a first transformation transforming the rhumb lines into straight lines, the construction of a path joining these positions while complying with the route constraints associated with these points, by means of arcs of circles and segments of straight lines tangential to the arcs of circles, the computation of the respective positions of the intermediate points spaced not far apart on said path, the application to said intermediate points of a transformation that is the reverse of said first transformation, so as to determine the geographical position of these intermediate points, and the automatic control of the piloting of the aerodyne so that its path flies over each of said intermediate points.