Abstract: New system for holding and fastening screws comprising a screw head provided with a mortise hole (1) having a tapered configuration along the screw longitudinal axis, said mortise hole (1) having a number of lugs (2) and the corresponding circular sections (3); and comprising a suitable screwdriver o fastening tool head tip (4) having a definite shape and wings (5), both according to the corresponding number of lugs (2) in order to match said screw head mortise hole (1); and comprising the required punching mortise die tool for the definite conformation of said screw head mortise hole (1) and said screwdriver or fastening tool head tip (4).