Satellite measurements of the magnetic anomaly field intensity have been used to estimate components of the vector field at the Earth's surface, using a linear approximation to relate satellite scalar measurements to downward-continued vector components. The relation between data and model was inverted using a depleted harmonic spline basis to find an almost minimum norm solution, enabling the detail present in satellite data to be preserved over continental-sized areas. In their development of the depleted basis method, Parker and Shure (1982) advocated using a subset of the original data as points in the depleted basis. Here, it is shown that a depleted basis formed from vertical component data kernels is much more satisfactory than a subset of measured intensity data kernels; however, we do form the depleted basis at the physical locations of actual data. The downward-continued map over Africa agrees well with its counterpart produced from Magsat orthogonal component data. ¿ American Geophysical Union 1996