Membrane for the tangential filtration of a fluid, said membrane comprising a porous support (2) delimiting at least one flow channel (3) for the fluid flowing in a given direction (f) between an inlet (6) and an outlet (7), the inner surface (4) of the porous support (2) which delimits channel (3) being coated with at least one separator layer (5) for the fluid, characterized in that the support has variable partial pore-filling (c) extending from the inner surface (4) of support (2) on which the separator layer (5) is deposited, said variable partial pore-filling creating a mean porosity gradient on portion (8) of support (2) of given constant thickness (e) extending from the inner surface (4) of support (2), the minimum mean porosity being located at the inlet (6) and the maximum mean porosity at the outlet (7).