This paper proposes a motion-planning method for a wrapping-with-fabric task. To wrap, robots require not only offhand paths (which represent the movement of a grasping point on fabric) but also actual robot motion. When a robot handles fabric, it must consider the range of motion and collisions. To overcome such limitations, the robot must pass fabric inter- and intra-hand. The proposition is based on the reliability of its movements. The method may be used to plan a combination of inter- and intra-hand passing motions to generate the basic movements for wrapping along an offhand path. Experiments show how, by using the proposed planning method, a dual-arm robot can wrap an L-shaped pipe.