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In this paper, a new method for fault location in power transmission lines is proposed. The idea of the introduced algorithm is that it considers the fault location problem as an optimization problem that can be solved by an appropriate mathematical method. Additionally, for finding the fault resistance the least-square estimation method is applied. The suggested technique only takes advantage of voltage and current samples taken at one end of the line and does not require filtering of DC offset and high-frequency components of the recorded signals, which are present during transient conditions. Computer simulations proved the accuracy of the proposed method in both cases of symmetrical and unsymmetrical faults. It is also shown that the accuracy of this method is not sensitive to fault inception angle and location of fault.