A truncated pyramid is usually used as a secondary optical element in the concentrated photovoltaic system. Usually, the total internal reflection (TIR) condition should be met twice in the design section when designing the truncated pyramid. However, the truncated pyramid is non-rotating axisymmetric relative to the optical axis. The propagation situation of the light in the non-design section is different with the one in the design section. The influence of the truncated pyramid′s non-rotating axisymmetry on the light TIR is studied with the vector method. It is proved that if a light in the design section meets the TIR condition twice, then setting the opposite sidewalls as a group, the light which has the same included angle with the axis in the non-design section meets the TIR condition twice in both groups. This provides a basis for the design of the truncated pyramid secondary optical elements.