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This paper proposes a differential quantization strategy to be used in the feedback link of a multi-input-multi-output (MIMO) communication system. This algorithm is applied to the channel correlation matrix exploiting geodesic curves and the intrinsic geometry of positive definite Hermitian matrices. Simulation results in the paper show that the proposed algorithm improves other techniques based on the direct quantization of the channel response matrix or the quantization of the subspace spanned by the strongest eigenmodes of the MIMO channel, i.e., Grassmannian based techniques. The main drawback of Grassmananian based algorithms is that the transmitter is constrained to apply a uniform power allocation among eigenmodes, which is not forced in the algorithm proposed in this paper.