Abstract: A weaving machine includes two temples whose axis is parallel to the weft threads and which are located at the lateral edges of the cloth, a cylindrical cloth-deflecting bar on which the cloth presses around an arc of contact before winding around a haul-off roll on which one or more backup rolls press. The clothdeflecting bar has a central cylindrical portion which connects coaxially on either side with two terminal portions next to the areas where the temples are installed, the terminal portions having a cross section which varies in shape proceeding from their ends adjacent to the central portion towards the free ends, causing a variation in the tension transmitted to the corresponding areas of the cloth by the hauloff roll, such that it varies from a minimum value at the ends of the terminal portions adjacent to the central portion to a maximum value at their free ends.