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Message propagation is a primary means to locate resources in current unstructured peer-to-peer (P2P) systems and how to reduce effectively the redundant messages of propagation while keeping its high network coverage is what many researchers go in for in this field. In this paper, we propose the algorithm of LMPR, a scheme of improved MPR for message propagation in distributed unstructured P2P system. Based on analyzing the process and message redundancy of MPR, this paper proposes to add to such scheme a mechanism of specified relay-list to reduce further the number of its retransmitting of message. By attaching to each relay-peer a relay-list with peers it will relay message to, the scheme can assure that in the view of each decision-peer a broadcast message can be dispatched and only be dispatched once to every neighbor peer within 2 hops of it. Simulation results show that the scheme of LMPR has better performance than that of MPR in message redundancy, network overhead, and fluctuation brought to the system. [ABSTRACT FROM AUTHOR]