The invention concerns a method for preparing a polymer, comprising a step which consists in contacting: (A) at least a living organic polymer having at its chain end a dithiocarbonylated or dithiophosphorylated function capable of being reactivated; (B) at least a source of free radicals; and (C) at least an organic compound bearing a labile hydrogen atom, whereby the dithiocarbonylated or dithiophosphorylated function present on said living organic polymer is substituted by a hydrogen atom.