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Shim describes unknown key-share attack on the server-specific MAKEP, and Siaw-Lynn Ng demonstrates further limitations of protocol. In the paper, we propose an improved version of server-specific MAKEP. The modified protocol not only overcomes the above attacks but also simplifies the protocol which proposed by Shim. Then, we analyze authentication of the improved protocol by extend theory of strand space. The analysis proved the correctness of the improved protocol.