A method of calculation, by a flight management system termed FMS, of a trajectory flown by an aircraft comprises the steps, calculated by the FMS, of: for at least one transition of the trajectory arising from the flight plan: 1) determining an initial transition comprising at least one arc exhibiting a single initial turning radius, 2) determining an initial trajectory incorporating the initial transition, 3) determining for each parameter a plurality of predicted values of the parameter in the course of the initial transition, 4) determining a plurality of ordered subdivisions of the arc of the initial transition according to a predetermined criterion, 5) determining, for each subdivision, an associated turning radius, 6) determining an improved transition on the basis of the ordered subdivisions and of the successive associated turning radii, 7) determining an improved trajectory incorporating the improved transition, 8) displaying the improved trajectory to a pilot of the aircraft.