A process for the extraction of hydrogen from a gas mixture including hydrogen and carbon monoxide and optionally nitrogen, carbon dioxide, lower hydrocarbons and/or water, by contacting the gas mixture with a non-porous polyimide-based membrane, especially with the selective side of an asymmetric membrane, to obtain a hydrogen rich permeate and a hydrogen lean retenate, the polyimide-based membrane being a specific mixture of two polyimids. This specific membrane shows a very high hydrogen/carbon monoxide selectivity. The process is especially suitable for the upgrading of synthesis gas obtained by partial oxidation and/or reforming of hydrocarbonaceous feedstream for use in hydrocarbon synthesis reaction as the Fischer-Tropsch reaction.