Non-imaging reflector may present the advantage to eliminate the dark image in beam down 2-stage optical concentrator. The working principle of the non-imaging secondary (NIS) for an axial symmetric concentrator is revealed. The geometrical shape of NIS can generally be high order surface not restricted to the quadratic one in imaging optics or the CPC in non-imaging optics. The article has described the method to determine the parameters of the curve. To break the tradition in optics, we have demonstrated in the article that beside the quadratic curve, cubic curve can be equally used to form NIS. In the respect of solar energy application, we have made the discussion on the behavior of NIS for solar disc effect and how a new parameter can be used to optimize the design.