A Bayer process comprises grinding and then digestion of bauxite by bringing it into contact with a sodium aluminate liquor. Digestion consists of forming a slurry that is then treated to separate insoluble residues from the sodium aluminate liquor. The liquor is then crystallized and recycled back to green liquor after having been separated from the alumina trihydrate precipitated during crystallization. The process comprises a predesilication treatment during which the ground bauxite, before digestion, is brought into contact with an aqueous sodic solution that has a content of carbonates, sulphates and possibly chlorides which, expressed as a percentage related to the caustic concentration, has less than half of the corresponding impurities content of the spent liquor. Preferably, the pure caustic soda used to compensate for caustic soda losses in the Bayer circuit, previously injected just after evaporation, is now added in the aqueous sodic solution for the predesilication treatment.