Lightning discharges emit very low frequency (VLF) radio waves commonly called atmospherics. In the past, lightning source locations were determined by the triangulation method from recordings at three widely separated stations in Japan. The three direction-of-arrival (DOA) lines, however, sometimes formed large triangles resulting in large uncertainties in source location. To approach this problem, the variational treatment is used here in which the sloping ionosphere plays an important role. By obtaining the time required to propagate from the source to the receiver via the Earth-ionosphere waveguide, it is found that the direction of propagation of a VLF wave can be bent along a parabolic curve. Using this concept of parabolic propagation, the locations of lightning discharges are compared with those determined by the triangular method. ¿ 2000 American Geophysical Union