The invention relates, firstly, to a method for eliminating ingested dietary fats before they are assimilated by the body, using an AGP extracted from cactus mucilage. Said AGP can be in any galenic or commercial form which is solid or dissolved in water. The invention also discloses the method of extracting this AGP from the mucilage of a cactus of the Platyopuntia genus, by means of a process which makes it possible to preserve the polysaccharide-protein association, which association is responsible for the observed activity.