The invention relates to a method for preparing linear polymers having an amide end or having a star architecture comprising an amide core, by means of a ring opening using lactide and glycolide monomers or a lactide monomer ring in the presence of a catalyst, wherein the method includes the steps of: (i) reacting the excess monomer(s) with an initiator in a solvent, said initiator being selected from among an amine and an amino alcohol, given that the initiator has at least one primary or secondary amine function; (ii) adding a catalyst, said catalyst being a non-nucleophilic base and including at least one neutral sp2 nitrogen atom; and (iii) neutralizing the reaction mixture. Said novel method is particularly advantageous in that it can be easily monitored and enables better modulation of the polymers, and thus of the properties thereof, than the methods of the prior art. The invention also relates to novel polymers that are obtainable by means of said method.