This onboard flight management system displays on the navigation screen the plots of the flight plan parts corresponding to the navigation procedures whose names are displayed on the MCD console during the introduction by the crew of the aircraft, by means of the MCD console, of the elements allowing the FMS flight management computer to plot a flight plan. This facilitates the task of the crew when choosing navigation procedure since the plot of the flight plan part corresponding to a navigation procedure is much more expressive than the name of the procedure.