A system for fastening an element, particularly made of fragile material such as glass, to a bearing structure or a framework at least at one point. At least at one fastening point, the system includes a mechanical connection device for fixing the element to a framework or bearing structure or connecting to an adjacent similar element. At least one arm at a first end is connected to a fastener mechanically connected to the element, and at a second end is connected to a joining piece. The joining piece includes a tubular envelope that contains a mechanism for adjusting degrees of freedom of the fixing or of the connection. A wall including at least one fixed or opening element can be fixed to a structure or a framework by such a mechanical connection device.