The invention concerns a strap or bracelet (1) including a first strand (2) and a second strand (3). The second strand (3) is connected to a clasp (1a) that includes a fastening device (13). The fastening device (13) joins the strands (2, 3) to each other. The invention is characterized in that the clasp (1a) further includes a safety device (17) for better joining the first strand (2) to the clasp (1a) by pressing the former onto the latter.