For enabling the manufacture of non-oriented steel strips by HDR, the amounts of AlN and MnS which precipitate on the way of HDR are decreased to such a level that they do not affect the magnetic properties by regulating the Al and S contents, and further unavoidable precipitating nitrides are precipitated as coarse BN. With regard to the steel composition, the amounts of C, Si and P are not only regulated, but also the amounts of Mn, Al, S and N are regulated from the above standpoint, and a proper amount of B is added if required. In addition, in regard to treatment conditions, in order to secure necessary finishing and coiling temperatures, the lower limit of the slab temperature at the starting time of HDR is specified. Moreover, to secure precipitation of BN and recrystallization of a ferrite structure, the lower limits of the finishing and coiling temperatures are specified. Furthermore, to secure the magnetic properties after cold rolling, the strips are finally continuously annealed at the determined temperature.