The cholesteric liquid crystal can be regarded as a multilayer structure consisting of many uniaxial thin films which exhibit optical rotation. A new method is proposed to study the polarization states of the transmitted light through a cholesteric liquid crystal. It is found that the cholesteric liquid crystal can completely change the polarization state of the transmitted light. The direction of linear polarization can be turned by 90°, and the left circularly polarized light can be translated into right one, when it passes through the cholesteric liquid crystal.