The present invention relates to a heddle (32) for a stretched fabric false wall provided with a harpoon that includes an inner arm, by means of which the harpoon is connected to the periphery of said fabric, and a curved outer arm, said heddle (32) including at least two peripheral vertical flanges (34) that extend downward and define at least one downwardly opening recess, and at least one shoulder (39) for receiving the bottom end of the outer arm when the fabric is stretched, said heddle (32) being characterized in that it includes two peripheral vertical flanges (34) and a central vertical flange (35), said flanges (34, 35) extending downward and defining two downwardly opening recesses, and in that each of said peripheral vertical flanges (34) includes a shoulder (39) on the inner surface thereof, and in that said central vertical flange (35) includes a shoulder (36) on each of the surfaces thereof.