The invention relates to a method and a system for aircraft navigation along a predetermined airway, including an on-board navigation system supplying a positioning integrity of the aircraft during flight relative to said airway respecting an expected position precision performance level, and at least one on-board radio receiver on the aircraft suitable for communicating with at least one land-based radio beacon suitable for supplying a distance of the aircraft relative to said radio beacon. The system includes a module configured to obtain, from a current position of the aircraft and stored data, a tuple of radio beacons to be used, a module configured to obtain a distance measurement of the aircraft relative to each of the N radio beacons of said tuple, a module configured to compute an integrity position from distance measurements obtained by a predetermined computing method, and a module configured to use the computed integrity position as current integrity position.