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Given the sensitivity of the potential WSN applications and because of resource limitations, key management emerges as a challenging issue for WSNs. One of the main concerns when designing a key management scheme is the network scalability. Indeed, the protocol should support a large number of nodes to enable a large scale deployment of the network. In this paper, we propose a new scalable key management scheme for WSNs which provides a good secure connectivity coverage. For this purpose, we make use of the unital design theory. We show that the basic mapping from unitals to key pre-distribution allows us to achieve high network scalability. Nonetheless, this naive mapping does not guarantee a high key sharing probability. Therefore, we propose an enhanced unital-based key pre-distribution scheme providing high network scalability and good key sharing probability approximately lower bounded by 1-e-1 ≈ 0.632. We conduct approximate analysis and simulations and compare our solution to those of existing methods for different criteria such as storage overhead, network scalability, network connectivity, average secure path length and network resiliency. Our results show that the proposed approach enhances the network scalability while providing high secure connectivity coverage and overall improved performance. Moreover, for an equal network size, our solution reduces significantly the storage overhead compared to those of existing solutions.