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In this paper we derive a novel method for encoding the MIMO channel state information (CSI) for frequency selective channels and limited feedback. The technique is based on the decomposition of the directional information of a MIMO channel in a two-coordinate system formed by the tangent space of a Grassmann manifold and the tangent space of a unitary group. The first component provides a non-redundant description of the subspace spanned by a set of channel eigenvectors, while the second component provides a non-redundant addendum of information to identify the strongest channel vector directions within that subspace. One advantage of this feedback representation is that it allows to exploit the correlation of MIMO channels by applying standard source coding techniques to the two coordinate components. We also provide simulation results of an LTE downlink system, which show that the proposed CSI feedback description offers dramatic throughput improvement over the existing feedback scheme for MU-MIMO transmission.