A new computer method of mapping the worldwide potential contours for ground magnetic perturbations is developed. The procedure includes the following steps: (1) the digitization of the magnetic perturbation values in (H,D) or (X,Y) coordinates by taking a suitable base level at each observatory, (2) the transformation from these coordinates into the common geomagnetic (Xm, Ym) system, (3) the interpolation of these field values to provide values at a regular network of points, and (4) the computations of the magnetic potential at each grid point to determine the associated current system in the ionosphere. This process involves the determination of the best potential field &PHgr; from the interpoalted H (Xm,Ym) values by solving the two-dimensional Poisson equation ∇2&PHgr;=%-div Hϑ,&lgr;(ϑ and &lgr; are colatitude and longitude, respectively) on the basis of the iteration method. Since the equipotential contour lines can be regarded as the equivalent ionospheric current lines, the contour maps are of great use in studying spatial and time changes of the substorm current system. Several examples of the magnetic potential obtained by the new method are shown, and a comparison with hand-drawn equivalent current systems proposed in the past is made. A series of potential contours is also shown to examine how the magnetic disturbance pattern changes during polar magenetic substorms. A preliminary examination of the computed potential patterns indicates an interesting recurrent feature of the polar magnetic substorm. That is, a significant part of the equivalent current flow originating in the westward auroral electrojet flows in the evening sector at middle and low latitudes. This characteristic is quite different from most of the substorm current systems proposed in the past, in which the 'return currents' from the westward electrojet flow only in the midnight and morning sectors.