The invention concerns a rubber composition useful for forming a tyre running tread, said composition being based on at least: a reinforcing inorganic filler; a diene elastomer having a molar percentage of units derived from conjugate dienes higher than 30 % which is prepared in emulsion and which includes carboxylic acid functions along its chain; a binding agent between said reinforcing inorganic filler and said elastomer consisting of a polysulphur alkoxysilane. Said composition is such that said elastomer is obtainable by carrying out: in an emulsifying solution, free radical copolymerisation of at least a conjugate diene monomer with a precursor comonomer which is hydrolysable or oxidizable in carboxylic acid, to obtain an intermediate diene elastomer comprising functions precursor of said acid along its chain; then hydrolysis or oxidation of said precursor functions to obtain said elastomer comprising carboxylic acid functions along its chain.