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In this paper we reduce the feedback overhead in two-stream MIMO with per stream link adaptation and codebook based precoding. The amount of feedback may be reduced by indicating the CQI of one stream in a differential manner. The performance of the system depends on how the differential feedback is designed. We optimize the differential feedback for the weaker data stream by considering an optimum differential quantization between the streams. The off-set CQI values for the weaker stream are found by maximizing the throughput on the weaker data stream using the distribution of the difference between the post processing SINR values of the streams. The SINR difference distribution is found in semi-analytic form for 2 times 2 MIMO with codebook based precoding and a linear receiver. The offset values are calculated for both i.i.d. and correlated flat Rayleigh fading channels for a given number of relative feedback bits.