A method for producing a sheet of paper or cardboard from a fibrous suspension, comprising the following steps: a) injecting a polymer P3 into a cellulose fiber suspension, b) forming a sheet of paper or cardboard, c) drying the sheet of paper or cardboard, the polymer P3 being prepared, prior to step a), from a water-soluble polymer P1 of at least one nonionic monomer selected from acrylamide, methacrylamide, N,N-dimethylacrylamide, and acrylonitrile, the P1 polymer being subjected to a Re1 reaction to give a P2 polymer, which is then subjected to a Re2 reaction to give the P3 polymer, which is injected into the fibrous suspension within 24 hours of the start of the Re1 reaction; - the Re1 reaction consisting in preparing a P2 polymer comprising isocyanate functions by reaction for 10 seconds to 60 minutes between (i) an alkali hydroxide and/or an alkaline-earth hydroxide, (ii) an alkali hypohalide and/or an alkaline-earth hypohalide and (iii) the polymer P1, the Re1 reaction being carried out at a temperature between 30°C and 60°C, with a coefficient Alpha = moles of hypohalide / moles of non-ionic monomer of the water-soluble polymer P1 is between 0.1 and 1.0 and a coefficient Beta = moles of hydroxide / moles of hypohalide is between 0.5 and 4.0, the P1 polymer having a weight average molecular weight between 100,000 and 20 million, - the Re2 reaction consisting in preparing a P3 polymer by reaction between (iv) a compound comprising at least one aldehyde function or a compound which can generate at least one aldehyde function, and (v) the P2 polymer comprising isocyanate functions, the Re2 reaction being carried out at a temperature between 10°C and 60°C, by adding to the P2 polymer between 2% and 50% of compound comprising at least one aldehyde function or of compound capable of generating at least one aldehyde function, % by weight with respect to the weight of the P2 polymer. a) injecting a polymer P3 into a cellulose fiber suspension, b) forming a sheet of paper or cardboard, c) drying the sheet of paper or cardboard, the polymer P3 being prepared, prior to step a), from a water-soluble polymer P1 of at least one nonionic monomer selected from acrylamide, methacrylamide, N,N-dimethylacrylamide, and acrylonitrile, the P1 polymer being subjected to a Re1 reaction to give a P2 polymer, which is then subjected to a Re2 reaction to give the P3 polymer, which is injected into the fibrous suspension within 24 hours of the start of the Re1 reaction; - the Re1 reaction consisting in preparing a P2 polymer comprising isocyanate functions by reaction for 10 seconds to 60 minutes between (i) an alkali hydroxide and/or an alkaline-earth hydroxide, (ii) an alkali hypohalide and/or an alkaline-earth hypohalide and (iii) the polymer P1, the Re1 reaction being carried out at a temperature between 30°C and 60°C, with a coefficient Alpha = moles of hypohalide / moles of non-ionic monomer of the water-soluble polymer P1 is between 0.1 and 1.0 and a coefficient Beta = moles of hydroxide / moles of hypohalide is between 0.5 and 4.0, the P1 polymer having a weight average molecular weight between 100,000 and 20 million, - the Re2 reaction consisting in preparing a P3 polymer by reaction between (iv) a compound comprising at least one aldehyde function or a compound which can generate at least one aldehyde function, and (v) the P2 polymer comprising isocyanate functions, the Re2 reaction being carried out at a temperature between 10°C and 60°C, by adding to the P2 polymer between 2% and 50% of compound comprising at least one aldehyde function or of compound capable of generating at least one aldehyde function, % by weight with respect to the weight of the P2 polymer. - the Re1 reaction consisting in preparing a P2 polymer comprising isocyanate functions by reaction for 10 seconds to 60 minutes between (i) an alkali hydroxide and/or an alkaline-earth hydroxide, (ii) an alkali hypohalide and/or an alkaline-earth hypohalide and (iii) the polymer P1, - the Re2 reaction consisting in preparing a P3 polymer by reaction between (iv) a compound comprising at least one aldehyde function or a compound which can generate at least one aldehyde function, and (v) the P2 polymer comprising isocyanate functions,