The present invention relates to a method by which a terminal feeds back channel state information for downlink transmission in a wireless communication system supporting multiple antennas. More specifically, the present invention comprises a step of transmitting a first precoding matrix index (PMI) and a second PMI for each sub-band, wherein a precoding matrix preferred by the terminal is instructed to combine the first PMI and the second PMI, and a precoding codebook in which a portion of a plurality of bits forming the second PMI is additionally used to form the first PMI is applied.