The gauze or leno harness comprises a frame-like carrier (2) for a crossing yarn (16) and a guide (4) for a standing yarn (7). A U-shaped guide or deflecting element (20) reciprocates the crossing yarn (16) between the two lanes (13 and 14) of the carrier (2), the crossing yarn (16) crossing the standing yarn (7) in its movements. The element (20) is borne with freedom of movement on the base of the passage (15) between the two lanes (13) and (14). Since the element (20) is freely movable, it cannot become sluggish as a result of becoming dirty.