A method and device for updating the position of an aircraft includes a flight management system incorporating first and second position supplying devices for supplying first and second positions during flight. The first position is based on inertial data and based on data from a satellite positioning system. The second position is based on inertial data and based on data from a radio-navigation system. The flight management system also includes an updating system that includes a fly over updating device, a radar updating device, and a take off updating device. The updating system is operable to generate an updating position manually or automatically that will be used as the second position and selected as a new position for use with the flight management system.