The invention relates to a method of producing a strip of
nanocrystalline material which is obtained from a wound ribbon that is cast in an amorphous state, having
atomic composition [Fe1-a-bCoaNib]100-x-y-2-alpha-beta-gamma Cu<x>Si<y>BzNbalphaM'betaM''gamma, M' being at least one of elements V, Cr, Al and Zn, and M being at least one of elements C, Ge, P, Ga, Sb, In and Be, with: a <= 0.07 and b = 0.1, 0.5 <= x <=1.5 and 2 <= a <= 5, 10 <= y <= 16.9 and 5 <= z <= 8, beta <= 2 and gamma <= 2. According to the invention, the
amorphous ribbon is subjected to crystallisation annealing, in which the ribbon undergoes annealing in the unwound state, passing through at least two S-shaped blocks under
voltage along an essentially longitudinal axial direction of the ribbon, such that the ribbon is maintained at an annealing temperature of between 530 DEG C and 700 DEG C for between 5 and 120 seconds and under axial tensile stress of between 2 and 1000 Mpa. The tensile stress applied to the
amorphous ribbon, the displacement speed of the ribbon during annealing and the annealing time and temperature are all selected such that the cross-section profile of the strip is not in the form of
Omega and the maximum deflection of the cross-section of the strip is less than 3% of the width of the strip and preferably less than 1% of the width. The invention also relates to the strip and the core thus obtained and to the device used to implement the method.