Abstract: This fastener comprises two elements (3, 4) connected to the band (1), the first element (3) including a pin (9) adapted to be fitted into retaining bearing surfaces (12) defined by hooks (13) on the second element (4), and a clasp (11) associated with the pin (9) and capable of being swung over and locked onto the second element (4). The second element (4) is provided with a safety hook (16) pivotally mounted on a transverse pin (10) of the second element and capable of being clipped onto the pin (9) of the first element (3) before the clasp (11) is swung over onto the second element (4). The fastener may be easily adjusted with one hand and does not require the provision of adjustment orifices on the band and hides the free end portion of the band, this end portion of the band being indeed interposed between the surface of the object surrounded by the band and the end portion (1a) of the band carrying the first element (3).