Analytical method is used to obtain the geometrical shape for non-imaging secondary (NIS) mirror in the application of concentrated photovoltaic (CPV). It is discussed in beam down optical system, NIS presents advantages to eliminate dark image, to reduce the solar disc effect, to improve the uniformity of the illumination, etc. comparing to the imaging secondary. The authors have emphasized that the geometrical shape of optical components in non-imaging optics can generally be high order surfaces not restricted to the quadratic surface in imaging optics and mostly "CPC" in early developed non-imaging optics. This paper has discussed the general criteria and two practical approaches for designing NIS. We listed some of the examples in this paper to form NIS by rotating a segment of linear or quadratic or cubic curve around the central axis of primary reflector. The method to calculate the parameters of such segment is described. Although in present discussion, we are referring the usage in PV concentrator, the method is generally applied in other optical fields. (C) 2013 Elsevier Ltd. All rights reserved.