The invention concerns an improved prosthesis component (1), for example an acetabular or glenoid cup (2) of an orthopedic prosthesis (12) or a liner constrained inside the cup (2) and intended to receive a spherical joint (4, 5) of an artificial femoral or humeral head (10), said component being substantially hemispherical- shaped with a base (6) defining the lower edge of the liner (1). Advantageously, according to the invention, the insert or liner (1) comprises a lip (8) projecting beyond the base (6)； in other words, the lip (8) projects beyond the equatorial line of the hemispherical form of the liner (1) partially occupying the missing hemisphere of the hemispherical form to define an undercut edge, as well as an extended portion (20) of said lip (8) by at least one tract of said base (6) in order to receive and hold a dual-mobility head in the spherical segment (9) inside the component (1, 1').
