Process for the continuous synthesis of a diene elastomer by means of n reactors r1 to rn, equipped with an internal stirring system, assumed to be perfectly stirred, and arranged in series, n ranging from 2 to 15, preferably from 2 to 9, the reactor r1 being fed by an input solution comprising a solvent, one or more monomers, an anionic polymerization initiator and a polar agent, one or more of the reactor(s) r2 to rn also being fed by reinjection of a purified solution comprising solvent and/or monomer(s), the purity of the or of each reinjected solution being such that the proportion of the number of dead chains in the output stream from the reactor rn is less than 30%, preferably less than 10%, of the number of living chains initiated in the reactor r1, the temperature of each reactor ranging from 20 to 150°C, preferably ranging from 30 to 120°C, and being greater than or equal to the temperature of the reactor which immediately precedes it, the temperature of the reactor rn being greater than the temperature of the reactor r1, - the weight amount Wi of monomer(s) introduced into the reactor r1 being such that 0.1 < W 1 ∑ i = 1 n Wi ≤ 1 the weight amount W i' of monomer(s) reinjected into the reactor ri', when W i' ≠0, i' ranging from 2 to n, being such that 0 ≤ Wi ′ ∑ 1 n Wi < 0.9 and such that Wi' represents from 5% to 100% by weight of the weight of the solution reinjected into the reactor ri', when W i' ≠0, where Wi is the weight amount of monomer(s) introduced into the reactor ri, i ranging from 1 to n, the weight amount of all of the monomers entering the reactors r1 to rn representing 5% to 25% by weight of the sum of the total weight inputs of the reactors r1 to rn, the overall weight conversion Ci" in each reactor ri" being such that Cn n − 0.2 < Ci " i " < Cn n + 0.2 where Ci " = Pi " ∑ 1 n Wi where Pi" is the weight of polymer formed at the output of the reactor ri", i" ranging from 1 to n-1, Cn is the overall weight conversion in the reactor rn, with Cn = Pn ∑ 1 n Wi where Pn is the weight of total polymer at the output of the reactor rn, the diene elastomer obtained having a polydispersity index ranging from 1.1 to 2, preferably between 1.1 and 1.7, more preferentially ranging from 1.2 to 1.6. - the weight amount Wi of monomer(s) introduced into the reactor r1 being such that 0.1 < W 1 ∑ i = 1 n Wi ≤ 1 the weight amount W i' of monomer(s) reinjected into the reactor ri', when W i' ≠0, i' ranging from 2 to n, being such that 0 ≤ Wi ′ ∑ 1 n Wi < 0.9 and such that Wi' represents from 5% to 100% by weight of the weight of the solution reinjected into the reactor ri', when W i' ≠0, where Wi is the weight amount of monomer(s) introduced into the reactor ri, i ranging from 1 to n, the weight amount of all of the monomers entering the reactors r1 to rn representing 5% to 25% by weight of the sum of the total weight inputs of the reactors r1 to rn, the overall weight conversion Ci" in each reactor ri" being such that Cn n − 0.2 < Ci " i " < Cn n + 0.2 where Ci " = Pi " ∑ 1 n Wi where Pi" is the weight of polymer formed at the output of the reactor ri", i" ranging from 1 to n-1, Cn is the overall weight conversion in the reactor rn, with Cn = Pn ∑ 1 n Wi where Pn is the weight of total polymer at the output of the reactor rn, the diene elastomer obtained having a polydispersity index ranging from 1.1 to 2, preferably between 1.1 and 1.7, more preferentially ranging from 1.2 to 1.6. the weight amount W i' of monomer(s) reinjected into the reactor ri', when W i' ≠0, i' ranging from 2 to n, being such that 0 ≤ Wi ′ ∑ 1 n Wi < 0.9 and such that Wi' represents from 5% to 100% by weight of the weight of the solution reinjected into the reactor ri', when W i' ≠0, where Wi is the weight amount of monomer(s) introduced into the reactor ri, i ranging from 1 to n, the weight amount of all of the monomers entering the reactors r1 to rn representing 5% to 25% by weight of the sum of the total weight inputs of the reactors r1 to rn, the overall weight conversion Ci" in each reactor ri" being such that Cn n − 0.2 < Ci " i " < Cn n + 0.2 where Ci " = Pi " ∑ 1 n Wi where Pi" is the weight of polymer formed at the output of the reactor ri", i" ranging from 1 to n-1, Cn is the overall weight conversion in the reactor rn, with Cn = Pn ∑ 1 n Wi where Pn is the weight of total polymer at the output of the reactor rn, the diene elastomer obtained having a polydispersity index ranging from 1.1 to 2, preferably between 1.1 and 1.7, more preferentially ranging from 1.2 to 1.6.