NOVELTY - The production of hydrogen from a hydrogen-rich feed gas in which N adsorbers are used, where N is greater than or equal to 1, comprises producing a flow of hydrogen with high cycle pressure in an adsorption phase, depressurizing and eluting the hydrogen at a low cycle pressure in a regeneration phase, and repressurizing the hydrogen at a high cycle pressure. During the depressurization step, a partial balancing of pressures is performed between adsorber at the start of the cocurrent depressurization and adsorber in the repressurization step until the pressure of the adsorber reaches a partial balancing pressure.    USE - The method is useful for purifying hydrogen and for recovering hydrogen from a low-pressure fuel network.    ADVANTAGE - The method economically produces hydrogen with high purity of 99 vol.%.    DETAILED DESCRIPTION - The production of hydrogen from a hydrogen-rich feed gas in which N adsorbers are used, where N is greater than or equal to 1, comprises producing a flow of hydrogen with high cycle pressure in an adsorption phase, depressurizing and eluting the hydrogen at a low cycle pressure in a regeneration phase, and repressurizing the hydrogen at a high cycle pressure. During the depressurization step, a partial balancing of pressures is performed between adsorber at the start of the cocurrent depressurization and adsorber in the repressurization step until the pressure of the adsorber reaches a partial balancing pressure and the flow exiting the adsorber undergoing cocurrent depressurization, which has a pressure lower than the partial balancing pressure, is sent to the adsorbers in the elution step. Part of the flows exiting the adsorbers in the regeneration phase is recycled by compressing the part until the high cycle pressure is reached and supplying the adsorbers in adsorption with the recycled part. The flow of hydrogen from the adsorber to depressurization step is introduced partly in an adsorber to the repressurization and the elution steps. The low pressure is less than or equal to 2 bars.    DESCRIPTION OF DRAWING(S) - The drawing shows the method of producing hydrogen from a hydrogen-rich feed gas using a pressure swing adsorption unit.    Gas supplying line (2)    Production line (3)    Waste gas evacuating line (4)    Recycling line (6)    Compression device. (8)