A method for the manufacture of a cold-rolled steel sheet of thickness ef between 0.5 mm and 3 mm is provided. At least two hot-rolled sheets of thickness ei are supplied and butt welded, so as to create a welded joint (S1) with a direction perpendicular to the direction of hot rolling. The at least two hot-rolled sheets are pickled by continuous passage through a bath, then the assembly is cold rolled, in a step (L1), to an intermediate thickness eint, the direction of cold rolling (DL1) coinciding with the direction of hot rolling. The cold rolling is carried out with a reduction ratio ɛ 1 = Ln ⁡ ( e i e int ) such that: 0 . 3 ⁢ 5 ≤ Ln ⁢ ⁢ ( ei e ⁢ ⁢ int ) Ln ⁢ ⁢ ( e ⁢ i e ⁢ f ) ≤ 0 . 6 ⁢ 5 , then the welded joint (S1) is removed so as to obtain at least two intermediate cold-rolled sheets. Then the two intermediate cold-rolled sheets are butt welded, so as to create a welded joint (S2), the direction of which is perpendicular to the direction of hot rolling, then the assembly of the at least two intermediate cold-rolled and welded sheets is cold-rolled, in a step (L2), to the final thickness ef, the direction (DL2) of the cold rolling step (L2) coinciding with the direction of rolling (DL1).