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