This paper puts forward a novel algorithm for locating faults on double-circuit transmission lines using two-end unsynchronized current measurements. The algorithm does not require line parameters, which is a radical step forward compared to existing approaches, which require this information, so it can be considered as a settings-free algorithm. Only the positive-sequence current phasors during the fault are processed for determining the sought distance to fault and the synchronization angle, limiting thus the amount of data needed to be transferred from each line terminal. The proposed algorithm is derived by applying the Kirchhoff's voltage law around the parallel circuits loops during the fault. The algorithm is applicable for both transposed and untransposed double-circuit lines and is independent of the fault type. Evaluation studies using reliable Alternative Transients Program-Electromagnetic Transients Program simulation data verify that the accuracy of the proposed algorithm is very high under various fault resistances, fault locations, and source impedances.