Method for picking loads from an automated storage/picking system comprising: • a steering system; • at least one storage set comprising several levels, whereon loads can be removed or deposited by shuttles; • at least one exit interface conveyor (70L, 80L) for loads exiting outside of the system; • an exit lift comprising K multiload levels, with K≥2, and presenting a climb/descent cycle; • an exit transfer device comprising K multiload levels; and • an exit sequencer provided with means of vertical displacement, the said method comprising the following steps: - at the time of an iteration of the said climb/descent cycle, transfer of a group of N loads, from the at least one multilevel storage set to the K multiload levels of the exit lift, with N less than or equal to a capacity of the exit lift in number of loads, and with, for each multiload level of the exit lift, a sequencing of loads, steered by the steering system, consistent with starting order limitation of N loads on said at least one exit interface conveyor; - transfer, simultaneously on the K levels, of the said group of N loads from the exit lift to the exit transfer device; and - transfer of the said group of N loads, via the exit sequencer, from the exit transfer device to the at least one exit interface conveyor, adhering to said starting order limitation of N loads on said at least one exit interface conveyor. • a steering system; • at least one storage set comprising several levels, whereon loads can be removed or deposited by shuttles; • at least one exit interface conveyor (70L, 80L) for loads exiting outside of the system; • an exit lift comprising K multiload levels, with K≥2, and presenting a climb/descent cycle; • an exit transfer device comprising K multiload levels; and • an exit sequencer provided with means of vertical displacement, the said method comprising the following steps: - at the time of an iteration of the said climb/descent cycle, transfer of a group of N loads, from the at least one multilevel storage set to the K multiload levels of the exit lift, with N less than or equal to a capacity of the exit lift in number of loads, and with, for each multiload level of the exit lift, a sequencing of loads, steered by the steering system, consistent with starting order limitation of N loads on said at least one exit interface conveyor; - transfer, simultaneously on the K levels, of the said group of N loads from the exit lift to the exit transfer device; and - transfer of the said group of N loads, via the exit sequencer, from the exit transfer device to the at least one exit interface conveyor, adhering to said starting order limitation of N loads on said at least one exit interface conveyor. - at the time of an iteration of the said climb/descent cycle, transfer of a group of N loads, from the at least one multilevel storage set to the K multiload levels of the exit lift, with N less than or equal to a capacity of the exit lift in number of loads, and with, for each multiload level of the exit lift, a sequencing of loads, steered by the steering system, consistent with starting order limitation of N loads on said at least one exit interface conveyor; - transfer, simultaneously on the K levels, of the said group of N loads from the exit lift to the exit transfer device; and - transfer of the said group of N loads, via the exit sequencer, from the exit transfer device to the at least one exit interface conveyor, adhering to said starting order limitation of N loads on said at least one exit interface conveyor.