1. A method of optimizing monitoring of a flight plan of an aircraft relative to a predetermined cost index predetermined by an operator, the flight plan including a determined set of waypoints to be overflown by the aircraft, the method implemented by a flight management system and comprising: computing an optimal flight plan based on the predetermined cost index and computing optimal values of an arrival time and of a quantity of fuel remaining on board that are estimated to destination for the optimal flight plan and the predetermined cost index, the optimal flight plan defining for said determined set of waypoints a longitudinal speed profile and a vertical trajectory; applying the optimal flight plan as the flight plan to be followed by the aircraft; and when at least one external constraint causes the flight plan followed by the aircraft to depart from the optimal flight plan, activating a corrective loop for overriding the flight plan to the predetermined cost index, wherein the corrective loop comprises: computing current values of the arrival time and the quantity of fuel remaining estimated to destination for the flight plan, detecting two differences including the difference of the current to the optimal values of an arrival time destination and the difference of the current to the optimal values of a quantity of fuel remaining on board at destination, determining a corrective cost index based on an overriding criteria minimizing each of the two differences, computing temporary corrections to the longitudinal speed profile and/or the vertical trajectory on at least a portion of the remaining flight plan based on said corrective cost index, applying the temporary corrections based on said corrective cost index on said at least portion of the remaining flight plan, and then applying the optimal flight plan based on the predetermined cost index for any remaining flight plan left.