The pile warp threads are passed through a storage means including a movable deflecting beam and two fixed bars which serve to form a thread reserve between two full beat-ups of the loom. A clamping beam cooperates with the bar of the storage means closest to the shed to clamp the threads during the time intervals between two successive beat-ups or between successive full and partial beat-ups. The opening of the clamping beam occurs simultaneously with the release of the thread reserve from the storage means to allow delivery of the pile warp threads without tension to the shed. This obviates any backward pull-out of the formed loop in the cloth.