The present invention provides a method for preparing a copolymer useful for the manufacture of tires by coupling the ends of a living polymer, obtained from copolymerization of a diene monomers in the presence of an organolithium initiator and a hydrocarbon solvent, with a multi-reactive polysiloxane compound, and subsequently modifying the remaining uncoupled ends of the polymer with an amine compound. The use of the copolymer thus obtained for tire production improves the affinity to silica and greatly enhances the dynamic properties required for tires, such as wet traction and rolling resistance.