A prosthesis member of a joint prosthesis for a thumb joint comprises a screw-like part (4) and an articulating socket element (6) with a mounting pin (9) which is insertable into a hole (8) in the screw-like part for attaching the articulating socket element thereto. The screw-like part (4) of the prosthesis member (2) is configured with a first fixing portion (15) which is provided with a first external thread (17) for attachment by screwing and fastening of said prosthesis member to the hard outer part (T1) of the trapezium (T), and a second fixing portion (18) having a less diameter than the diameter of the first fixing portion and being provided with a second external thread (19) which is configured to permit attachment by screwing and fastening of said prosthesis member to the soft inner part (T2) of the trapezium. The first fixing portion (15) is provided with a surface (20) which connects the threads (17, 19) on said fixing portions (15, 18) to each other and which converges substantially arcuate towards the second fixing portion (18). Hereby, optimum fixation of the prosthesis member (2) in the trapezium (T) is achieved.
