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In this paper, we propose a novel iterative greedy reconstruction algorithm, called iterative pseudo-inverse multi-plication (IPIM), for fast reconstruction of the target signal in Compressive Sensing (CS). Compared with the state-of-art greedy algorithms such as CoSamp and SP, IPIM need not calculate the pseudo-inverse at a cost of O(K2M) at each iteration, where the sparsity K means that the N-length signal can be approximated by K coefficients, and M is the length of the measurement. No matter how big the sparsity K is, the iteration complexity of IPIM maintains O(MN). In order to obtain the same reconstruction quality, computational experiments show that IPIM spends much less time than the competing algorithms when K is relatively large especially K >; √N.