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This paper presents a new low complexity method of providing improved channel state information at the transmitter within closed-loop MIMO systems. We propose to feedback the second best codeword in addition to the best codeword. At the transmitter, these two precoding codewords are interpolated using geodesic. The optimal interpolation parameter is derived in closed-form for single-stream transmission. The performance of the proposed method with b-bit codewords is shown to be close to a codebook with 2b-bit codewords, while our method has significantly lower computational complexity.