A rapidly quenched Fe-based soft-magnetic alloy ribbon having wave-like undulations on a free surface, the wave-like undulations having transverse troughs arranged at substantially constant intervals in a longitudinal direction, and the troughs having an average amplitude D of 20 mm or less, is produced by a method comprising (a) keeping a transverse temperature distribution in a melt nozzle within 15 C. to have as small a temperature distribution as possible in a melt paddle of the alloy, and (b) forming numerous fine linear scratches on a cooling roll surface by a wire brush, thereby providing a ground surface of the cooling roll with an arithmetical mean (average) roughness Ra of 0.1-1 m and a maximum roughness depth Rmax of 0.5-10 m.

A rapidly quenched Fe-based soft-magnetic alloy ribbon having wave-like undulations on a free surface, the wave-like undulations having transverse troughs arranged at substantially constant intervals in a longitudinal direction, and the troughs having an average amplitude D of 20 mm or less, is produced by a method comprising (a) keeping a transverse temperature distribution in a melt nozzle within 15 C. to have as small a temperature distribution as possible in a melt paddle of the alloy, and (b) forming numerous fine linear scratches on a cooling roll surface by a wire brush, thereby providing a ground surface of the cooling roll with an arithmetical mean (average) roughness Ra of 0.1-1 m and a maximum roughness depth Rmax of 0.5-10 m.