Two algorithms have been developed at Rice University for optimal linear feature extraction based on the minimization risk (probability) of misclassification under the assumption that the class conditional probability density functions are Gaussian. One of these algorithms, which applieds to the case in which the dimensionality of the feature space (reduced space) is unity, has been described elsewhere [Rice University ICSA Technical Reports Nos. 275-025-022 and 275-025-025 (EE Technical Reports Nos. 7520 and 7603)]. In the present report, we describe the second algorithm which is used when the dimension of the feature space is greater than one. Numerical results obtained from the application of the present algorithm to remotely sensed data from the Purdue C1 flight line are mentioned. Brief comparisons are made of these results with those obtained using a feature selection technique based on maximizing the Bhattacharyya distance. For the example considered, a significant improvement in classification is obtained by the present technique.