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Transmission network expansion planning (TNEP) is a very important problem in power systems. It is a mixed integer, non-linear, non-convex optimisation problem, which is very complex and computationally demanding. Various meta-heuristic optimisation techniques have been tried out for this problem. However, scope for even better algorithms still remains. In view of this, a new technique known as harmony search is presented here for TNEP with security constraints. This technique has been reported to be robust and computationally efficient compared to other meta-heuristic algorithms. Results for three sample test systems are obtained and compared with those obtained with genetic algorithm and bacteria-foraging differential evolution algorithm to verify the potential of the proposed algorithm.