This method is for weaving a fabric with warp yarns and in-woven weft yarns (34) on a weaving loom which comprises, amongst others, a weft selector (28) and a weft insertion mechanism (20), for drawing-in a weft yarn from a pick-up position into the shed, along a weft insertion axis (Y20) and in a forward direction, the weft insertion mechanism including a gripper (40) openable at the pick-up position. This method includes at least the following steps: opening the gripper; positioning a movable carriage (102) of the weft selector so that the gripper (40) is aligned with a selected weft yarn (34); clamping the weft yarn in the selected distribution channel (130), with the clamp (164) of this channel; moving the weft yarn (34) along the selected distribution channel (130) toward the gripper (40), while the gripper is opened, by moving the clamp along the selected distribution channel; catching the selected weft yarn with the gripper at the pick-up position; drawing-in the weft yarn with the weft insertion mechanism, from the pick-up position into the shed, along the weft insertion axis and in the forward direction; and cutting the weft yarn. The weft selector defines several selectable distribution channels (130) parallel to the weft insertion axis (Y20), each selectable distribution channel including a forward guiding member (126), for guiding a weft yarn toward the gripper, and a clamp (164).
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