A filter for the filtration of a fluid such as a liquid, comprising or composed of a support element (1) made of a porous ceramic material, said element exhibiting a tubular or parallelepipedal shape delimited by an external surface (2) and comprising, in its internal portion (3), a set of adjacent channels (4) with axes parallel to one another and separated from one another by walls (8) of said porous inorganic material, in which at least a portion of said channels (4) and/or at least a portion of said external surface are covered with a porous separating membrane layer (5), said filter being characterized in that: - said separating membrane layer is made of a material essentially composed of silicon carbide (SiC), - the content by weight of elemental nitrogen of the layer constituting the porous separating membrane layer is between 0.1% and 2%.