A fiber bundle which has a pieced part formed by jetting a pressurized fluid against a fiber-bundle overlap is formed either by directly superposing the ending part of a fiber bundle composed of many fibers on the beginning part of another fiber bundle composed of many fibers or by superposing the end part and the beginning part on a jointing fiber bundle composed of many fibers, whereby the many fibers of the fiber bundles are interlaced with one another to thereby piece up the fiber bundles. The pieced part comprises an opened-fiber part in which the fibers have been opened and interlaced-fiber parts respectively located on both sides thereof, each interlaced-fiber part being composed of a plurality of constituent interlaced parts located apart in the width direction for the fiber bundle.