Material for stainless steel sheets is heated to a temperature within a range of 850 to 1250.degree. C. and cooled at a rate 1.degree. C./s or faster, the material including 0.02% by mass or less of C, 1.0% by mass or less of Si, 2.0% by mass or less of Mn, 0.04% by mass or less of P, 0.01% by mass or less of S, 0.1% by mass or less of Al, 11% by mass or more but less than 17% by mass of Cr, 0.5% by mass or more but, less than 3.0% by mass of Ni, and 0.02% by mass or less of N, so as to satisfy specific relationships between the compositions.