A new design is described for an unobscured, all-reflective laser beam expander. It has very high performance and can be designed for any desired beam expansion ratio. Since the components are just spherical mirrors, the cost of making this design is much less than the cost of making a confocal parabola beam expander, especially in large sizes. The key to the high performance and reasonable length of this new design is the use of a simple and very powerful design principle that can be applied to other types of beam expanders as well. An example is given of a 1.0 meter aperture 30X expander design.