The present invention concerns a method for preparing a polymer comprising a step of radical polymerization of monomers comprising at least monomers (M1) chosen from acrylic acid, one of the salts of same, or the mixture thereof, in which said radical polymerization step is carried out: continuously; at a pH which remains between 3 and 5 during the polymerization step; in the presence of a metabisulfite/persulfate redox pair, for example the sodium metabisulfite/sodium persulfate pair, as a radical initiator, with a metabisulfite/persulfate molar ratio of between 1 and 3.5 and an initiator/monomer molar percentage of between 5% and 18%.