A cast slab containing C: less than 0.02 mass% and made of an Fe-based metal of an ± - ³ transforming component is subjected to hot rolling at a temperature of an A3 point or higher and is subjected to ±-region rolling at a temperature of 300°C or higher and lower than the A3 point, and thereby a base metal sheet having a {100} texture in a surface layer portion is fabricated. Then, by performing a heat treatment under predetermined conditions, an Fe-based metal sheet is obtained in which a Z value is not less than 2.0 nor more than 200 when intensity ratios of respective {001}<470>, {116}<6 12 1>, and {223}<692> directions in a sheet plane by X-ray diffraction are set to A, B, and C respectively and Z = (A + 0.97B)/0.98C is satisfied.