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Many applications of wireless sensor network (WSN) require secure data communications, especially in a hostile environment. In order to protect the sensitive data and the sensor readings, secret keys should be used to encrypt the exchanged messages between communicating nodes. Traditional asymmetric key cryptosystems are infeasible in WSNs due to the low capacity of each senor node. In this paper, we propose a new key pre-distribution scheme for hierarchical WSNs. Compared to some of the existing schemes, our methods possess the following features that are particularly beneficial to the resource-constrained large-scale WSNs: (1) it can fully defend against the node captured attack, (2) it minimizes the storage and communication overhead, and (3) it provides full connectivity of the network.