Abstract: A method and device for continuously grinding the teeth of a number of adjacent saw bands using a rotating grinding wheel which is reciprocatingly moveable in a direction transverse to the longitudinal direction of the saw bands. The method comprising lowering the grinding wheel at the start of each reciprocating grinding movement a predetermined distance which corresponds to wear the grinding wheel experienced in the prior grinding cycle. As the grinding wheel is moved towards the band material, it is acted on by a stationary abrasing wheel which reshapes the grinding wheel. During the return stroke of the grinding wheel the saw band blanks are advanced and repositioned for another cycle of the grinding wheel.