A bearing providing at least two rings able to pivot relative to one another, at least one of the rings including at least two annular ring parts having annular radial surfaces axially opposite each other. The bearing further providing at least one annular shim disposed between the radial surfaces of the annular ring parts and including successive circumferential portions. Each circumferential portion of the shim has a plurality of nicks respectively traversed by axial elements. The nicks of each circumferential portion of the annular shim are shaped and oriented to permit the positioning between the annular ring parts and the removal of each circumferential portion by radial translation.