An anti-vibration arrangement for a band saw blade in a band saw machine, which is constructed to cut a workpiece by shifting the endless band saw blade running in a circulating manner to a cutting direction, wherein nozzles are provided for injecting high-pressure cutting liquid toward each side face of the body of the band saw blade on the entering-side where the band saw blade enters into a cut groove of the workpiece formed by the band saw blade in the cutting process of the band saw machine.