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This paper proposes a new key management scheme for wireless sensor networks to reduce the memory and communication overhead, and improve the security capacity. Comparing with the typical key pre-distribution schemes, a new method of establishing keys is adopted, and is analyzed deeply in three important performance indexes. The theory of liner combination is applied to generate the keys using the random vectors in vector group. In order to validate such positive effects of the proposed scheme, simulations are performed on the software of Matlab7.1. The results of simulations demonstrate that the proposed scheme has better performances to improve the resilience to node capture of the networks and reduces the memory and communication overhead than that of key pre-distribution schemes.