A gripper pulls a web off a supply downstream through upstream and downstream clamps. The upstream clamp is closed on the web and a piece is cut off its end. Then the gripper is moved back upstream to form the cut-off piece into a dependent loop while the lower part of the downstream clamp is held down and back out of the way so it does not contact the dependent loop. Once the gripper has moved upstream passed the lowered downstream clamp part, it is raised and advanced downstream to press the web against the upper downstream clamp part. Then both clamps are displaced transversely to move the web as a dependent loop transversely away.