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: M.sub.xSiAl.sub.yO.sub.a(OH).sub.b, (H.sub.2O).sub.c (I) in which: M is a cation selected from of K.sup.+, Na.sup.+, Ca.sup.++ and mixtures of these cations; x>0; y>0; a.gtoreq.0; b.gtoreq.0, c.gtoreq.0 and a+b>0, and having the following characteristics: (a) a BET specific surface area of between 20 and 300 m.sup.2/g; (b) an average particle size by mass (d.sub.w) of between 20 and 400 nm; and (c) an ultrasound disagglomeration rate (.alpha.) greater than 5.times.10.sup.-4 .mu.m.sup.-1/min.