This paper proposes a non-contact method for fault location in transmission lines, which is based on magnetic fields produced by current signals measured using magnetoresistive sensors installed only at transmission line terminals, under the phase conductors of the first transmission tower at both terminals or at the substations portals. The proposed method uses the Extended Kalman filter to process these measurements and is based on a travelling wave approach in order to perform the fault localization. This paper also describes the implementation and testing of the method, firstly introducing its overview, followed by an analysis of the magnetic fields produced by the current signals, as well as considerations on their measurement; secondly, detailing the Extended Kalman filter and the travelling wave approach; and, finally, presenting the results of the method with regards to simulations built using EMTP/ATP to evaluate its robustness under different conditions varying the fault resistance, fault inception angle, phases involved and fault location. The results indicate that the proposed method is robust and accurate.