A polyaxial bone fastener assembly (1) comprising a plate (2) with at least one through orifice (3), and at least one fastener screw (4) for fastening the plate (2) to a bone, the body (6) of the screw (4) being suitable for passing through the orifice (3), and its head (5) being suitable for being retained in the orifice (3) of the plate (2) by bearing contact between complementary male and female spherical surfaces (7, 8), the female spherical surface (8) that is arranged in the orifice (3) of the plate (2) forming a seat within which the male spherical surface (7) is suitable for coming to bear when the screw (4) is inserted in the orifice (3).On going from the bottom face (22) towards the top face (21) of the plate (2), the bore of the orifice (3) in the plate (2) comprises: an inner collar (9)； a cylindrical portion (10)； and the seat-forming female spherical surface (8)； and on going between its male spherical surface (7) and its zone (11) connecting to the body (6) of the screw (4), the head (5) of the associated fastener screw (4) has a threaded portion (12) with a single-start thread, the thread being interrupted in at least two zones (13) in order to enable the inner collar (9) of the orifice (3) in the associated plate (2) to be machined while the screw (4) is being driven to turn inside said orifice (3) until it reaches a position of bearing contact between the male and female spherical surfaces (7, 8).
