This prosthesis (1) includes: two pairs (2, 3) of elongated joint elements (6-9) forming disc joint surfaces (6e-9e) and facet joint surfaces (6b-9b) means (10a, 10b, 11a, 11b) for positioning one pair (2, 3) of elements relative to the other. According to the invention, each disc joint surface (6e-9e) is in the shape of a hemisphere portion said positioning means comprise posterior positioning surfaces (10a-11b) the prosthesis is associated with at least one rigid transverse element (4, 5) comprising positioning surfaces designed to be placed against said posterior positioning surfaces (10a-11b), this placement making it possible to perform relative positioning of one pair of joint elements (6, 8) relative to the other pair of joint elements (7, 9) such that the disc joint surfaces (6e, 7e, 8e, 9e) are situated in a same geometric hemisphere (H).
