A method of automatic piloting of an aircraft during a phase of approach to a predetermined airdrop position includes automatically applying a speed profile with decreasing speed such that the aircraft will reach the airdrop position at a predetermined theoretical arrival time with a predetermined speed, the speed profile having a plurality of constant-speed levels separated by deceleration phases. An actual arrival time is automatically determined and a difference between the theoretical and actual arrival times is calculated. If the calculated difference differs from zero, the speed profile is corrected by modifying the length lengths of time that at least two constant-speed levels are applied to the aircraft so as to cancel the difference.