In a typical conventional slitting machine, a rolled raw material is fed by a feeder, then slit into strips having a desired width or widths by a cutter at one stage of the process for feeding the material, and then rewound on a rewinding shaft. For rewinding the required number of strips, a corresponding number of rewinding drums are locked to only one rewinding shaft by suitable means such as a key so that the drums are prevented from slipping and thereafter, the strips are fixedly rewound on the rewinding drums.