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Provided are a method and a device for producing an Si-containing cold-rolled steel sheet having excellent chemical treatability, even using a low-temperature chemical treatment solution, with which sludge formation is maintained to a minimum and running costs are reduced. The method comprises a step whereby steel containing 0.5 to 3.0 mass% of Si is cold rolled, the product is subjected to continuous annealing, and then the surface of the continuously annealed cold rolled steel is washed with acid, and a step whereby the surface of the steel sheet that has been washed with an acid is re-washed with an acid using a nonoxidizing acid. The solution used for re-washing with an acid is continuously or periodically sampled and the acid concentration of the sample is determined in order to always maintain the acid concentration of the solution for re-washing with an acid within a predetermined concentration range.