A porous inorganic membrane comprises at least one inorganic phase having separating properties. Said membrane has a carbon content representing 0.05% to 25% by weight with respect to the mass of said inorganic phase and is selective to non-condensable gases. It is obtained by means of a selectivation treatment of a porous carbon-free inorganic membrane using a hydrocarbon feed. It is used in processes for separating non-condensable molecules such as hydrogen, and in association with a catalyst in a catalytic membrane reactor.