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In wireless sensor networks, sensor nodes eventually die due to battery depletion. Wireless sensor networks (WSNs) in which new nodes are periodically redeployed with certain intervals, called generations, to replace the dead nodes are called multi-phase wireless sensor networks. In the literature, there are several key predistribution schemes proposed for secure operation of WSNs. However, these schemes are designed for single phase networks which are not resilient against continuous node capture attacks; even under temporary attacks on the network, the harm caused by the attacker does not heal in time. However, the periodic deployments in multi-phase sensor networks could be utilized to improve the resiliency of the WSNs by deploying nodes with fresh keys. In the literature, there is limited work done in this area. In this paper, we propose a key predistribution scheme for multi-phase wireless sensor networks which is highly resilient under node capture attacks. In our scheme, called RGM (random generation material) key predistribution scheme, each generation of deployment has its own random keying material and pairwise keys are established between node pairs of particular generations. These keys are specific to these generations. Therefore, a captured node cannot be abused to obtain keys of other generations. We compare the performance of our RGM scheme with a well-known multi-phase key predistribution scheme and showed that RGM achieves up to three-fold more resiliency. Even under heavy attacks, our scheme's resiliency performance is 50% better in steady state.