The inventive composition is based on cerium oxide and on zirconium oxide in an atomic proportion Ce/Zr of at least 1, and has a reducibility rate of at least 70% and a surface area of at least 15 m; 2; /g. This composition is obtained by a method in which: a mixture is made containing cerium and zirconium compounds; this mixture is provided with a basic compound whereby obtaining a precipitate that is heated in an aqueous medium; a surfactant-type additive or a polyethylene glycol or a carboxylic acid is added to this medium or to the separated precipitate; the mixture is ground; the precipitate obtained thereof is calcined under inert gas or vacuum, in a first period of time, at a temperature of at least 850 .iC and then under an oxidizing atmosphere, in a second period of time, at a temperature of at least 400° C.