Method for cold rolling of a high magnetic flux density grain-oriented electrical steel sheet or strip having excellent properties

In a cold rolling method for producing a high magnetic flux density grain oriented electrical steel sheet or strip comprising the steps of hot rolling a silicon steel material containing 2.5 to 4.0% Si, not more than 0.085% carbon and 0.010 to 0.065% acid soluble Al, annealing the hot rolled steel sheet at a temperature between 950.degree. and 1200.degree.C and rapidly cooling the steel sheet to precipitate AlN, subjecting the steel sheet to a one-step heavy cold rolling at a reduction rate between 81 and 95 percent to obtain a final sheet thickness, decarburization annealing of the cold rolled steel sheet, and final annealing, the improvement which comprises obtaining the final steel sheet or strip thickness by a plurality of rolling passes of the heavy cold rolling through various interim sheet thicknesses and holding the steel sheet at a temperature between 100.degree. and 350.degree.C for at least 1 minute during the heavy cold rolling step at least one time between the above plurality of rolling passes.