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In this work, a novel fault-locator technique for two- and three-terminal power transmission lines is introduced. Unsynchronized three-phase current and voltage measurements of all line ends are processed for estimating the required synchronization angle/s and the fault location via exploiting the initial conditions of each fault type. To realize this target, the computations of the required synchronization angle/s are initially accomplished independent of the fault location via considering a lumped charging current at the reference terminal which is selected arbitrarily. Consequently, the initial fault location is determined via equating the deduced equations of the positive-sequence voltage at the faulty point from two sides of the faulted segment as a function of the measured data after their correction. The previous obtained fault location is, then, utilized as an input for the next iterative computations, where the distributed line model is used to update the charging current. This process is repeated until the change rate of the obtained fault location becomes negligible. The proposed technique has been examined and assessed under different fault scenarios simulated using MATLAB. The sample results of the assessment are declared and discussed.