A method for manufacturing such steel sheet includes continuous annealing of a steel sheet which includes, in terms of mass %, C at 0.01 to 0.18%, Si at 0.4 to 2.0%, Mn at 1.0 to 3.0%, Al at 0.001 to 1.0%, P at 0.005 to 0.060% and S at ≦0.01%, the balance being represented by Fe and inevitable impurities, in such a manner that the dew point of the atmosphere is controlled to become not more than −45° C. during the course of soaking when the annealing furnace inside temperature is in the range of not less than 820° C. and not more than 1000° C. as well as that the dew point of the atmosphere is controlled to become not more than −45° C. during the course of cooling when the annealing furnace inside temperature is in the range of not less than 750° C.