Device for forming a selvedge on a fabric comprising at least one thread guiding element (8-9) for what is called a leno thread (10-11), provided on an arm (16), whereby this thread guiding element (8-9) can be moved by means of a drive mechanism (24), characterised in that the drive mechanism (24) comprises the combination of an oscillating drive element (25); coupling parts (26), and a mechanism (27) with which the movement of one of the above-mentioned coupling parts (26) can be translated in a lateral movement of the above-mentioned thread guide (17-18).