A method using a continuous annealing furnace where a cooling method of a cooling zone including part or all of the temperature range of the steel sheet of 600 to 250° C. following the heating for recrystallization is one or more of gas cooling, effusion cooling, and cooling pipe cooling, or a joint cold rolled steel sheet/hot dip galvanized steel sheet facility having such a continuous annealing furnace, to continuously anneal cold rolled steel sheet to produce high strength cold rolled steel sheet, characterized by exposing the steel sheet surface to an iron-oxidizing atmosphere in the steel sheet temperature range to make the surface oxidize, pickling the sheet at the outlet side of the annealing furnace, then iron- or Ni-plating the sheet to 1 to 50 mg/m2.