Machine for manufacturing buttons comprising: - a base; - a container device, supported on the base, capable of containing a plurality of disc-shaped elements to be machined on the machine; - a supplying device, operatively connected to the container device, capable of selectively supplying, by fall through a channel, a single disc-shaped element at a time to a clamp gripping device; - a clamp gripping device, fixed to the base, provided with two opposite and coaxial gripping shafts (22, 24), which block said disc-shaped element by pressure, acting onto its two opposite and parallel surfaces, and set it into rotation; - a machining device, fixed to the base and arranged adjacent to the clamp gripping device, capable of machining the outer circumferential edge of said disc-shaped element held and made to rotate by said clamp gripping device; and - a self-centering positioning system of the disc-shaped elements, arranged on the clamp gripping device below the supplying device, capable of positioning each disc-shaped element, independently from its outer diameter, substantially coaxially with respect to the opposite gripping shafts (22, 24) of said clamp gripping device, the machine being characterised in that said self-centering positioning system comprises a supporting plate substantially vertical and arranged perpendicularly to the axis of the gripping shafts (22, 24), said supporting plate being provided with a circular through hole which allows one of said gripping shafts to cross said supporting plate in the blocking step of the disc-shaped element, on the front surface of the supporting plate being applied an upper holding wall, arranged above said circular through hole, and two lateral holding walls (60, 62), arranged respectively on the left and on the right of said circular through hole, capable of receiving each disc-shaped element that is supplied by fall by the supplying device, as well as capable of guiding said disc-shaped element towards a stop means arranged below said circular through hole, wherein both the lateral holding walls (60, 62), and the stop means are mounted on respective pins (66, 68; 70) mobile with a linear motion along respective guiding slots (72, 74; 76) obtained in the supporting plate, the movement of said pins (66, 68; 70) and, as a consequence, of the lateral holding walls (60, 62) and of the stop means being obtained through an elastic actuating mechanism arranged below said supporting plate. - a base; - a container device, supported on the base, capable of containing a plurality of disc-shaped elements to be machined on the machine; - a supplying device, operatively connected to the container device, capable of selectively supplying, by fall through a channel, a single disc-shaped element at a time to a clamp gripping device; - a clamp gripping device, fixed to the base, provided with two opposite and coaxial gripping shafts (22, 24), which block said disc-shaped element by pressure, acting onto its two opposite and parallel surfaces, and set it into rotation; - a machining device, fixed to the base and arranged adjacent to the clamp gripping device, capable of machining the outer circumferential edge of said disc-shaped element held and made to rotate by said clamp gripping device; and - a self-centering positioning system of the disc-shaped elements, arranged on the clamp gripping device below the supplying device, capable of positioning each disc-shaped element, independently from its outer diameter, substantially coaxially with respect to the opposite gripping shafts (22, 24) of said clamp gripping device,