A screw with a variable locking angle into a bone plate, where the said screw comprises: - a screw head with curved surfaces and contact surfaces, as well as a centrally placed star-shaped socket for receiving a fastening tool, located on the upper side of said head; and - a screw body ending with a tip that enters the bone first; where the said screw body is equipped with a self-cutting thread which extends from the joint between the screw head and the screw body to the tip of the screw, - where the said screw head is formed from a rotationally symmetric truncated cone of height h, with a base radius Rout on which said star-shaped socket is centrally positioned and where the cone side is inclined at an angle Y relative to the axis of said cone which coincides with the screw axis; - where n equally curved surfaces, n ≥ 4, are carved into said cone and extend from the upper edge of the screw head to the bottom edge of the said head and where each of the said surfaces forms a portion of the cylindrical surface with the curvature Rc, where the longitudinal axis of said cylindrical surface lies on the straight line Π which is parallel to the cone surface and inclined at an angle Y relative to the axis of the screw, and where the intersections of all straight lines Π of the said n cylindrical surfaces with the plane perpendicular to the screw axes form vertices of a regular polygon with n sides; - where the said curved surfaces are interconnected with the identical contact surfaces of the truncated cone, both extending from the upper edge to the bottom edge of the screw head; - where the upper edge is partly formed from the points of contact surfaces that lie on the radius Rout with the center on the axis of the screw, and from the upper edges of the curved surfaces in a way that the highest point of each surface lies on the radius Rin in a plane parallel to the plane containing the base of the radius Rout, provided that Rin < Rout; and - where the bottom edge is formed from the ends of contact surfaces and the curved surfaces so that it enters the joint between the head and the screw body; characterized by that the screw head, with curved surfaces and contact surfaces, is formed without any thread on the said surfaces (24, 25). - a screw head with curved surfaces and contact surfaces, as well as a centrally placed star-shaped socket for receiving a fastening tool, located on the upper side of said head; and - a screw body ending with a tip that enters the bone first; where the said screw body is equipped with a self-cutting thread which extends from the joint between the screw head and the screw body to the tip of the screw, - where the said screw head is formed from a rotationally symmetric truncated cone of height h, with a base radius Rout on which said star-shaped socket is centrally positioned and where the cone side is inclined at an angle Y relative to the axis of said cone which coincides with the screw axis; - where n equally curved surfaces, n ≥ 4, are carved into said cone and extend from the upper edge of the screw head to the bottom edge of the said head and where each of the said surfaces forms a portion of the cylindrical surface with the curvature Rc, where the longitudinal axis of said cylindrical surface lies on the straight line Π which is parallel to the cone surface and inclined at an angle Y relative to the axis of the screw, and where the intersections of all straight lines Π of the said n cylindrical surfaces with the plane perpendicular to the screw axes form vertices of a regular polygon with n sides; - where the said curved surfaces are interconnected with the identical contact surfaces of the truncated cone, both extending from the upper edge to the bottom edge of the screw head; - where the upper edge is partly formed from the points of contact surfaces that lie on the radius Rout with the center on the axis of the screw, and from the upper edges of the curved surfaces in a way that the highest point of each surface lies on the radius Rin in a plane parallel to the plane containing the base of the radius Rout, provided that Rin < Rout; and - where the bottom edge is formed from the ends of contact surfaces and the curved surfaces so that it enters the joint between the head and the screw body;