A new computer-based ELF/VLF system for locating lightning discharges has been developed. Both the arrival azimuths of atmospherics and the distances to their sources are estimated. The direction-finding technique uses the Poynting vector calculated directly in the time domain over the full band pass of the receiver. Both the distance of the lightning discharge and the ionospheric height can be estimated from the phase spectrum of the first-order mode of the Earth-ionosphere waveguide. The latter is approximated with a model function having the distance and the height as the main parameters. Two ways were applied to obtain the spectrum of the first mode: the radial component of the horizontal magnetic field was used, which contains only a minor component of the zeroth mode, or the mode decomposition problem was solved. The system has been used to locate lightning sources in Africa and Asia from a scientific vessel during its voyage in the Atlantic and Indian Oceans in 1991. The overall uncertainties are estimated to be a few degrees for the source bearing, 5% for distance, and 1% for the effective height of the ionosphere; yet these estimates need an additional confirmation by comparison with independent and more exact techniques.