Many existing pairwise key establishment in sensor networks were developed based on the polynomial-based method. However, this method cannot offer the basic authentication function of security. In this paper, we develop a novel tame-based approach to achieve the goal of authentication. We then present a general framework , for pairwise key establishment, in the basis of this tame-based approach. It turns out that this tame map can substitute the polynomial in any existing polynomial pool-based scheme to offer the authentication service. In particular, we further introduce a new scheme, local symmetric-tame maps predistribution scheme, based on this framework. The analysis demonstrates that, in addition to being able to provide authentication service, this scheme not only has significantly better performance, but also can achieve greater resilience on security than existing schemes. Keywords-Sensor networks, tame automorphism, key management, network security