A flight management assembly for an aircraft includes at least one flight management system and at least one display device, the flight management system configured to manage at least one flight plan of the aircraft and one long-term reference path of the aircraft. The flight management assembly additionally includes an auxiliary computer, the auxiliary computer being separate from and independent of the flight management system, the auxiliary computer linked to the flight management system and to the display device, the auxiliary computer configured to perform prediction computations to generate at least one short-term path, from at least the long-term reference path received from the flight management system and from current flight parameters of the aircraft and from piloting setpoints of the aircraft.