A method for monitoring the flight trajectory of an aircraft comprises the steps reiterated in time consisting in receiving and comparing two trajectory objects, the trajectory objects being associated with two initially identical flight trajectories determined independently of each other over time; and, in case of difference between the two trajectory objects, determining a failed trajectory from the two flight trajectories by comparison with the last known state without fault, the last known state without fault corresponding to two identical trajectory objects. Developments describe the use of flight plan segments, of signatures, fault isolation simultaneously to a change of current leg, the use of levels of operational safety according to an RNP-AR procedure and the notification of the pilot of the trajectory determined as having failed. Software and system aspects are also described.