Abstract: In a method for fitting a preassembled pulley subassembly (1) on a rotary machine (2), the preassembled subassembly comprising a pulley (7), a rolling bearing (8), a plate (9) and an elastic ring (23) positioned around a shoulder (9a) of the plate (9), the following steps are carried out:—the bearing (8) is mounted on a hollow shaft (10) of the rotary machine (2) and, at the same time, a hub (20) of the plate (9) is mounted on a rotary spindle (4) of the rotary machine (2), that passes through the hollow shaft (10),—the elastic ring (23) of the plate (9) is slid axially until it enters a groove (10a) in the hollow shaft (10) of the rotary machine.