An approximate maximum likelihood technique employing a widely available (BMD) discriminant analysis program has been developed for resolving the percentage of component terrains within single resolution elements. The method employs all four channels of Landsat data simultaneously and does not require prior knowledge of the percentage of components in mixed pixels. For five test cases, the method proved to be superior to single band weighted average and linear regression techniques and permitted an estimate of the total area occupied by component terrains to within 6 percent of the true area covered. It is believed this accuracy should be sufficient for many geologic applications of Landsat multispectral data.