The invention relates to a method for assembling parts (P1 and P2) in composite hardware by means of a riveting member (R), and is notable in that it comprises: using a bushing (200), the hollow core (230) of which has two different sections (231 and 232); using an insert (100) having no functional axial bearing surface for the radial swelling of the bushing (200) in the through-hole (T), but the diameter (D3) of which is capable of enabling the housing thereof, with no change in shape, in the first section (231) of the hollow core (230), and is also capable of enabling the forcible housing thereof in the second section (232); axially feeding the insert (100) into the bushing (200) such that the latter radially swells inside the through-hole (T) up to the small section (232) thereof and such that the recess well-defined by said small section is occupied by said insert (100); and ensuring, by means of a rivet set (400), the pressure on the first section (231) of the bushing (200) by the end that changes shape to ensure the bending thereof by radial centrifugal extension.