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In unitary precoded multi-antenna systems with delayed feedback, the quantized channel state information (CSI) may become outdated before its actual use at the transmitter. In this letter, by exploiting the geometric properties of the Grassmannian manifold, we invoke the use of Grassmannian subspace predictive coding (GSPC) to overcome this problem. Under the framework of GSPC, a novel limited feedback strategy is proposed which consists of a two-stage optimization process at the receiver. The first stage quantizes the estimated CSI by accounting for the feedback delay; while the second stage optimizes the prediction on the Grassmannian manifold.