Directional overcurrent elements, both phase and ground, are widely used as backup protection for transmission lines in interconnected power systems around the world. Traditionally, the specialized literature has focused on the determination of the time dial settings of such elements for improving selectivity, as well as the polarization method to be used, for improving security; leaving the directional characteristic settings, and more specifically, the determination of the directional characteristic angle, to the application of the so-called typical settings. This setting, most commonly known as Maximum Torque Angle (MTA) or Relay Characteristic Angle (RCA), is the basis for the direction determination algorithm. Therefore, it is of paramount importance to establish a methodology for its proper calculation. The main contribution of this paper is an alternative methodology to stablish the MTA/RCA settings of directional overcurrent relays, by using a detailed shortcircuit sensitivity analysis and a non-linear optimization technique. The application of this novel approach on real complex transmission systems increases the reliability of directional overcurrent protection elements, and has shown that the values required by the actual fault conditions of the transmission system could present a large deviation from the so-called typical settings.