Suitable methods of multivariate statistical analysis have already been shown to be useful to overcome the topographic effect which arises when employing remotely-sensed data in rugged terrain. In the present work the application of these techniques to Gaussiam maximum likelihood classifications is examined. As the maximum likelihood classifier takes into account the internal relations in the multivariate data set, it is generally insensitive to the topographic effect provided that the training points are uniformly distributed with respect to variations in solar illumination angle. On the other hand, the conventional classifier does not perform well if such an assumption is not valid, because the spectral distribution of the training data becomes far from normal and not representative of the original situation. In this case a modification of the classifier which eliminates the information related to the first principal component of the data set of each class can be efficient. The difference in discrimination accuracy between the classical and modified classifications is appreciable when they are applied to extreme situations; an example shows that this difference, evaluated by means of the Kappa coefficient of agreement, may be high and statistically significant