An apparatus for cleaning the edges of a magnetic tape cut into final-product widths from a wide raw material web with which magnetic powder shed from the tape and base film dust breaking off in the cutting process are removed without damage to the tape. The apparatus includes an air bearing guide for floating the magnetic tape as it is transported thereon, a cleaning device positioned at a side of the guide and making contact with at least one edge of the magnetic tape, and a magnet device for urging the edge of the tape into close contact with the cleaning device.