The normalized polarimetric classifier which uses only the relative magnitudes and phases of the polarimetric data is proposed for discrimination of terrain elements. For polarimetric data with arbitrary probability density function, the distance measures of the normalized polarimetric classifer based on a general class of normalization functions are shown to be equivalent to one another. When the system absolute calibration factors are common to all polarimetric channels, the normalized polarimetric classifer derived is shown to be optimal. Further assuming a complex Gaussian distribution of the unnormalized data, the distance measure of the normalized polarimetric classifer is given explicitly and is shown to be independent of the number of scatters illuminated. The usefulness of the normalized polarimetric classifier is demonstrated by the classification of grass and tree regions in experimental data obtained from the Massachusetts Institute of Technology Lincoln Laboratory. The classification errors generated using the optimal normalized polarimetric classifer are shown to be smaller than those generated using other types of classifiers which employ only magnitude ratios or phase differences to classify radar images. ¿ American Geophysical Union 1988