A method and device for aiding the piloting of an aircraft while respecting a time of arrival constraint at a first waypoint during a phase of descent. The method includes calculating an instant of arrival of the aircraft at an intermediate waypoint, in such a way that an estimated latest time of arrival at the first waypoint, corresponding to a minimum speed profile, occurs later by a predetermined first margin than the time of arrival constraint; determining a first speed profile between a current position of the aircraft and the intermediate waypoint, such that the intermediate waypoint is crossed at the calculated instant of arrival; determining a second speed profile, such that the first waypoint is crossed within the time of arrival constraint, starting from the intermediate waypoint at the calculated instant of arrival; and piloting the aircraft according to the first and then second speed profiles.