Abstract: An improved band saw blade for cutting hard ferrous or non-ferrous articles, wherein the band saw blade comprises an elongated, flexible, continuous ribbon having a back edge and a toothed edge, the ribbon having a sinoidal pattern in the plane of the ribbon, the wavelength and pitch of the ribbon being selected to enhance the cutting of the article but is selected to avoid chatter based on the rate of speed of travel of the ribbon, the pressure applied to the ribbon during the cutting and the average length of the cut to be made in the article to be cut. A method of constructing a band saw blade with a sinoidal pattern including the steps of successively squeezing portions of the saw blade or ribbon alternately near its back edge and near its toothed edge, whereby the blade is formed with a continuous wave pattern.