Abstract: A power driven screw driver self-gripping composite bit in the form of a pair of mirror image halved elements united at a common oblique interface providing a square end driver for reception in a screw head formed with a combined socket that accepts both a square end bit and a cross-point bit. Each halved element driver portion defines a trapezoidal cross section having major and minor parallel exterior side surfaces, a complete side surface extending at right angles to its major and minor surfaces, and a diagonal-like interface. The composite bit holder resiliently biases the halved elements interfaces into coextensive flush contact normally defining a square end driver.