The system (10) for assisting the piloting of an aircraft (1) comprises a flight management computer (12) and a guidance computer (18). The flight management computer transmits speed instructions to the guidance computer so as to pilot the aircraft according to an initial speed profile or, according to an RTA speed profile following receipt of an RTA constraint. In response to reception of a setpoint speed selected by a crew member in the presence of the RTA constraint, the guidance computer controls the aircraft according to the selected speed and the flight management computer determines a deselection point allowing the return to a predetermined speed profile while respecting the RTA constraint. The guidance computer controls the display, on a navigation screen (20), of a symbol (PS, PS1, PS2) corresponding to the position of the deselection point.
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