A method for manufacturing a metal outer bearing race having a reference axis, the method comprising: - the placing of a blank between dies (10, 12) of a forging tool; - a relative bringing together of the dies (10, 12) parallel to the reference axis so as to delimit a cavity comprising an internal zone and at least three auricular zones extending radially outwards from the internal zone, each of the three auricular zones comprising a bottom zone constituting a material-escape space, and so as to form an unfinished piece by deformation of the blank in the cavity, the unfinished piece comprising a central portion and an annular portion surrounding the central portion, the central portion and the annular portion occupying the internal zone of the cavity, the unfinished piece further comprising lugs projecting radially outwards from the annular portion, each inside a corresponding one of the auricular zones, each of the lugs comprising flanks in contact with walls of the dies (10, 12) and an external radial end portion situated radially outside the flanks, the annular portion having peripheral walls extending between the lugs and turned radially outwards in contact with walls of the dies (10, 12), and - a finishing of the outer bearing race, characterised in that - the relative bringing together of the dies (10, 12) parallel to the reference axis is such that the external radial end portion of each of the lugs partially fills a material-escape space formed by the bottom zone of each of the corresponding auricular zones, - the relative bringing together of the dies (10, 12) parallel to the reference axis is such that the unfinished piece has peripheral flash line portions, corresponding to a joint face between the dies (10, 12) and extending over the flanks of the lugs and over the peripheral walls of the annular portion; - the finishing of the outer bearing race includes machining of the unfinished piece out of the forging tool with the disappearance of the end portion of each of the lugs and the formation, for each of the lugs, of a reworking surface turned radially outwards, but without making the peripheral flash line portions on the flanks of the lugs and on the peripheral walls of the annular portion disappear, so that the outer race after finishing comprises the peripheral flash line portions. - the placing of a blank between dies (10, 12) of a forging tool; - a relative bringing together of the dies (10, 12) parallel to the reference axis so as to delimit a cavity comprising an internal zone and at least three auricular zones extending radially outwards from the internal zone, each of the three auricular zones comprising a bottom zone constituting a material-escape space, and so as to form an unfinished piece by deformation of the blank in the cavity, the unfinished piece comprising a central portion and an annular portion surrounding the central portion, the central portion and the annular portion occupying the internal zone of the cavity, the unfinished piece further comprising lugs projecting radially outwards from the annular portion, each inside a corresponding one of the auricular zones, each of the lugs comprising flanks in contact with walls of the dies (10, 12) and an external radial end portion situated radially outside the flanks, the annular portion having peripheral walls extending between the lugs and turned radially outwards in contact with walls of the dies (10, 12), and - a finishing of the outer bearing race, characterised in that - the relative bringing together of the dies (10, 12) parallel to the reference axis is such that the external radial end portion of each of the lugs partially fills a material-escape space formed by the bottom zone of each of the corresponding auricular zones, - the relative bringing together of the dies (10, 12) parallel to the reference axis is such that the unfinished piece has peripheral flash line portions, corresponding to a joint face between the dies (10, 12) and extending over the flanks of the lugs and over the peripheral walls of the annular portion; - the finishing of the outer bearing race includes machining of the unfinished piece out of the forging tool with the disappearance of the end portion of each of the lugs and the formation, for each of the lugs, of a reworking surface turned radially outwards, but without making the peripheral flash line portions on the flanks of the lugs and on the peripheral walls of the annular portion disappear, so that the outer race after finishing comprises the peripheral flash line portions.