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Authentication test is a formal method of verifying the security protocols based on strand space model. However, it hardly analyzes some complex security protocols on account of its poor cryptographic primitives. This paper proposes one way of extension of authentication test based on strand space model. First, message term, the in-term relation and penetrator model in strand space model are extended. Then; three concepts of transformed edge, transforming edge and test component in authentication test are extended. Eventually, TLS1.0 handshaking protocol is analyzed with the proposed approach, and property of authentication is verified.