A new method to reconstruct the instantaneous convection pattern in the Earth's polar ionosphere is suggested. Plasma convection in the polar cap ionosphere is described as a hydrodynamic incompress-ible¯ow. This description is valid in the region where the electric currents are ®eld aligned (and hence, the Lorentz body force vanishes). The problem becomes two-dimensional, and may be described by means of stream function. The¯ow pattern may be found as a solution of the boundary value problem

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... r stream function. Boundary conditions should be provided by measurements of the electric ®eld or plasma velocity vectors along the satellite orbits. It is shown that the convection pattern may be reconstructed with a reasonable accuracy by means of this method, by using only the minimum number of satellite crossings of the polar cap. The method enables us to obtain a reasonable estimate of the convection pattern without knowledge of the ionospheric conductivity.