A method for manufacturing a strip having a variable thickness along its length, comprising the steps: an initial strip of constant thickness is provided; homogeneous cold rolling of the initial strip along its length in order to obtain an intermediate strip of constant thickness along the rolling direction; flexible cold rolling of the intermediate strip along its length in order to obtain a variable thickness strip, having, along its length, first areas with a first thickness (e+s) and second areas with a second thickness (e), less than the first thickness (e+s), continuous annealing of the strip. The plastic deformation ratio generated, after an optional intermediate recrystallization annealing, by the homogeneous cold rolling and the flexible cold rolling steps in the first areas is greater than or equal to 30%.