We first discuss quantitative rules for determining the protein structural classes based on their secondary structures. Then we propose a modification of the least Mahalanobis distance method for prediction of protein classes. It is a generalization of a quadratic discriminant function to the case of degenerate covariance matrices. The resubstitution tests and leave-one-out tests are carried out to compare several methods. When the class sample sizes or the covariance matrices of different classes are significantly different, the modified method should be used to replace the least Mahalanobis distance method. Two lemmas for the derivation of our new algorithm are proved in an appendix.