A method of reporting a channel state to a base station supporting downlink multiple input multiple output in a wireless communication system includes measuring a downlink channel based on a downlink signal received from the base station, and reporting a codebook index for precoding of the downlink signal according to the measurement of the downlink channel. The codebook for precoding includes an improved codebook (hereinafter, referred to as an improved 4Tx codebook) having a dual structure composed of a codebook for wideband and a codebook for subband, for 4 transmit (4Tx) antenna ports, and the improved 4Tx codebook includes sub-codebooks obtained by sub-sampling the codebook for subband according to priority.