In this paper an overhead lines protection numerical algorithm, based on one terminal data and derived in the time domain, is presented. The fault location, direction and its nature (arcing or arcless fault) are estimated using Least Error Squares Technique. The faulted phase voltage is modeled as a serial connection of fault resistance and arc voltage, offering by this the more sophisticated line protection. The algorithm can be applied for both the ordinary and the high impedance faults detection, distance protection, intelligent autoreclosure, as well as for the purpose of directional relaying. The approach presented does not require the line zero sequence resistance as an input datum. The algorithm is derived for the case of most frequent single-phase to ground unsymmetrical faults. The results of algorithm testing through computer simulation are given. The influence of remote infeed, fault resistance, higher order harmonies, power system frequency, network topology, line parameters and other factors are investigated and systematically presented. Finally, an example of real life data processing is given.