Paleomagnetism provides data useful for reconstructing the former positions of the continents. Conventionally, reconstructions were performed by constraining the continental blocks to latitude circles defined by paleomagnetic data, while the longitudinal positions were chosen arbitrarily. We propose a new method of reconstruction based on the geophysical inverse theory, in which models are evaluated by the combined effects of misfit and penalty, the latter being given by some physical reasoning. We allow misfits in reconstruction within the uncertainties given by the statistical parameters of paleomagnetic data. For the penalty function, we propose to minimize the total slip of blocks accompanied with the movements over the surface of the earth. The method is formulated and then applied to the simple two-plate problem of the opening of the North Atlantic. Although the reconstruction looks reasonable, there is certain discrepancy between the obtained model and the Bullard et al. fit of Europe and North America. The reason for this discrepancy as well as other practical problems in obtaining the reconstructions are discussed.