An acetabular reamer (10, 10′, 10″) is intended in particular for the shaping of the cotyloid cavity in the event of a replacement of a hip joint by total prosthesis. The reamer (10, 10′, 10″) is typically of a truncated hemispherical form and is adapted for attachment to a reamer spindle in order to be driven in rotation about a cutter axis (11). The ability to cut a full, continuous hemisphere to the apex (12) of the hemispherical body (14) is suppressed, so as to attain the principal advantage of the invention, namely, to adequately prepare the acetabulum for receipt of a prosthesis while minimizing the possibility of breakthrough of the fovea/acetabular fossa. The reamer (10, 10′, 10″) has an interface 16 typically made tip of cross bars (20) which a holder engages for rotationally activating the reamer for cutting.