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It's well known that the dominant subspace of the time-varying channel matrix for MIMO system can be treat as a point in Grassmann manifold. The beamforming using Grassmannian subspace packing (GSP) codebook is based on this view, which feedback the index of the codeword for a limited feedback. But if there is channel time-domain correlation, GSP scheme can not utilize the correlation. A scheme can utilize the correlation for subspace tracking: 1bit feedback scheme quantize the geodesic trajectory connecting two subspaces to reduce the feedback bits number. But the convergence speed of this scheme constraint the performance of 1 bit feedback scheme. So we propose a new beamforming algorithm, which extracts advantages of both schemes, reduces the feedback rate and enhances the system performance. Simulation results show that the new algorithm has a better performance than GSP scheme with the same feedback bits number, and solve the problem of the performance descend for 1bit feedback scheme.