This paper describes the theory, design and fabrication of a complementary pair of cone-like mirrors which transform an annular collimated laser beam into a gaussian profiled collimated beam without obscuration. The details of a simple computer algorithm are revealed which explain the numerical procedure for computing the coordinates of the mirror surfaces. Also discussed is the procedure to diamond turn the nonlinear surfaces using the development lathe at the ERDA Y 12 Plant and the metrology of the first parts produced.