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 monomer and a vinyl aromatic monomer in the presence of an organolithium catalyst and a hydrocarbon solvent with a multi-reactive polysiloxane compound and then modifying the remaining uncoupled ends of the polymer with an amine compound. The use of the copolymer thus obtained for the fabrication of tires improves the affinity to silica as well as carbon black used as a reinforcing material and provides enhanced properties required for tires, such as increased wet traction, reduced rolling resistance, and increased tread wear.