Key distribution is one of the most challenging issues for secure communication in wireless sensor networks. Even though the random key pre-distribution approach is suitable for sensor nodes of low power and resource, a shared key between a pair of nodes is not guaranteed to be found and thus they cannot communicate with each other. This paper proposes a new robust key pre-distribution scheme solving this problem while security is not compromised even though the data exchanged between the nodes are tapped by an adversary. This is achieved by using the keys assigned through LDU decomposition of the symmetric matrix of a pool of keys. A general form solution of L, D, and U matrix is also developed to minimize the time overhead of LDU decomposition. Computer simulation reveals that the proposed scheme also significantly improves the energy efficiency compared with the existing random key pre-distribution scheme.