A transmission gearbox (1) has a casing (2) that tilts around a tilting axis (B--B) via two bearings (19). Each of the bearings includes: a fixed part (20) having a sleeve (20a); and a trunnion (21a) which belongs to a pivoting part (21) and which pivots around the sleeve, the pivoting part being solidly connected to the casing (2). A shouldered wear ring (22) is disposed between the sleeve (20a) and the trunnion (21a) of each bearing (19). The invention is suitable for use in the pivot mounting of a power transmission gearbox (1) that is used to rotate the tilting rotor (14) of a convertible aircraft.