An onboard flight management system in an aircraft comprises means for continuously calculating first geolocation data, from data received from at least one external geolocation device, comprising a current position and future positions of an aircraft along a trajectory sequenced in several portions and comprising second data comprising demands required by an international navigation procedure called “Required Navigation Performance”, or RNP, for all the portions of the trajectory. The management system additionally comprises a means for displaying first and second data all the way along the trajectory, the first and second data being represented graphically and simultaneously on the said display means in order to enable the pilot to anticipate the flight characteristics for the aircraft and make them converge toward the required demands of the next trajectory portion.