A rubber composition usable for the manufacture of tires, based on at least one diene elastomer, one reinforcing inorganic filler and a coupling agent providing the bond between the inorganic filler and the elastomer. The inorganic filler comprises a synthetic aluminosilicate of the formula: MxSiAlyOa(OH)b, (H2O)c  (I) in which: M is a cation selected from of K+, Na+, Ca++ and mixtures of these cations; x>0; y>0; a≧0; b≧0, c≧0 and a+b>0, and having the following characteristics: (a) a BET specific surface area of between 20 and 300 m2/g; (b) an average particle size by mass (dw) of between 20 and 400 nm; and (c) an ultrasound disagglomeration rate (α) greater than 5×10−4 μm−1/min.