A method for the manufacturing of high strength cold rolled steel sheets includes continuously annealing a cold rolled steel sheet that has a composition containing C: 0.05-0.3% mass, Si: 0.6-3.0% mass, Mn: 1.0-3.0% mass, P: ≦0.1% mass, S: ≦0.02% mass, Al: 0.01-1% mass, N: ≦0.01% mass, and Fe and inevitable impurities: balance, in a manner such that the cold rolled steel sheet is heated in a furnace using an oxidizing burner to a steel sheet temperature of ≧700° C., then soak-annealed in a reducing atmosphere furnace at 750-900° C., then cooled so the average cooling rate between 500° C. and 100° C. is ≧50° C./s. High-Si cold rolled steel sheets with high strength and good phosphatability while containing Si≧0.6% are obtained without controlling conditions so as to increase the dew point in the reducing atmosphere in the soaking furnace or to increase the vapor hydrogen partial pressure ratio.