A method for producing a sheet of paper or cardboard from a fibrous suspension, includes injection of a polymer P2 into a fibrous suspension, forming of a sheet of paper or cardboard, and drying the sheet of paper or cardboard. The polymer P2 is prepared, before injection of the polymer P2, from a water-soluble polymer P1 in the form of solid particles. Polymer P1 consists of at least one nonionic monomer selected from acrylamide, methacrylamide, N,N-dimethylacrylamide, and acrylonitrile. Polymer P1 is subjected to a reaction Re to yield polymer P2. The reaction Re includes the addition and the dissolution of solid particles of polymer P1 in an aqueous solution M1 of an alkali hydroxide and/or an alkaline earth hydroxide, and an alkali hypohalide and/or an alkaline earth hypohalide, prior to a reaction time of 10 seconds to 5 hours.