A synthetic method consisting of: (a) combining a composition containing an aprotic solvent and a water-soluble amine-terminated or hydroxy-terminated polymer with a composition containing an activated carbonate reagent selected from the group consisting of di (1-) carbonate benzotriazolyl), disuccinimidyl carbonate, pnitrophenyl chloroformate, trichlorophenyl chloroformate, p-nitrophenylsuccinimidyl carbonate, p-nitrophenyl-1-benzotriazolyl carbonate, pentafluorophenyl chloroformate and 1,1'-carbonylimide in the presence of a catalyst an acid neutralizing base, where the composition containing the activated carbonate reagent is added such that there is an excess of the activated carbonate reagent relative to the water-soluble amine-terminated or hydroxy-terminated polymer, in order to obtain a composition containing an active carbonate ester of the water-soluble polymer and ac carbonate reagent unreacted tivate, and (b) add, before recovering the active carbonate ester of the water-soluble polymer, a composition containing a reactive molecule selected from the group consisting of water, a lower alkyl monohydric alcohol, hydrogen sulfide and an amine monobasic alkyl lower than the composition containing the active carbonate ester of the water-soluble polymer and unreacted activated carbonate reagent, where the composition containing a reactive molecule is added such that more than 50% carbonate reagent is consumed activated not reacted.Un método sintético consistente en: (a) combinar una composición que contiene un solvente aprótico y un polímero hidrosoluble acabado en amina o acabado en hidroxi con una composición que contiene un reactivo de carbonato activado seleccionado entre el grupo consistente en carbonato de di(1-benzotriazolilo), carbonato de disuccinimidilo, cloroformiato de pnitrofenilo, cloroformiato de triclorofenilo, carbonato de p-nitrofenilsuccinimidilo, carbonato de p-nitrofenil-1- benzotriazolilo, cloroformiato de pentafluorofenilo y 1,1'-carbonil
