The invention relates to a method for producing anionic polymers that are hydrosoluble in an aqueous solution, comprising at least the following successive steps: b) polymerisation, in an aqueous solution, of anionic monomers containing at least 5 mol % of 2-acrylamido-2-methylpropane sulfonic acid and/or one of the salts thereof and optionally non-ionic monomers up to a mass concentration of polymer A of between 5 and 40%, b) addition of at least one aldehyde into the solution produced in step a), and c) acidification to a pH of between 3 and 4 of the solution produced in step b). The invention also relates to the use thereof in a paper-making method.