The invention relates to a system which is used to replace ball bone joints. The inventive system consists of: a bone anchoring shell (1) comprising a smooth articular surface (7) on the inner concave face thereof; a prosthesis (5) comprising a polished ball (4) and a neck (6) which is characterised in that it is smooth and slightly flared, in order to enable a wear-free low friction movement; and a mobile articular cup (3) which slides (i) on the ball (4) and the neck (6) of a prosthesis (5) and (ii) in the smooth cavity (7) of the bone anchoring shell (1) and which is characterised in that the opening (8) in said cup (3) tapers towards the centre thereof, with an inside diameter (9) of equal to or less than that of the ball (4), such that the flared part adapts perfectly to the flared neck (6) in all of the respective positions of the mobile parts.