The one-dimensional objective procedure for detecting and then correcting errors arising in geophysical data, developed in the previous paper of this series, is extended to higher dimensions. The data again must be sampled at equal increments of time or distance, but the spacings can be different in each dimension. Of interest are only those errors larger in magnitude than the background noise level. Errors occurring in isolation, clusters, and corners are treated as in the first paper; however, the appropriate generalizations to higher dimensions are developed in detail. Underlying the success of the error detection and correction procedure is the alternating subset method, which is extended to higher dimensions. Complete step-by-step instructions are given for the two-dimensional procedure. Finally, a two-dimensional example is presented to demonstrate the kinds of improvements afforded by the procedure.