The development of prediction methods based on statistical theory generally consists of two parts: one is focused on the exploration of new algorithms, and the other on the improvement of a training database. The current study is devoted to improving the prediction of protein structural classes from both of the two aspects. To explore a new algorithm, a method has been developed that makes allowance for taking into account the coupling effect among different amino acid components of a protein by a covariance matrix. To improve the training database, the selection of proteins is carried out so that they have (1) as many non-homologous structures as possible, and (2) a good quality of structure. Thus, 129 representative proteins are selected. They are classified into 30 α, 30 β, 30 α + β, 30 α/β, and 9 ζ (irregular) proteins according to a new criterion that better reflects the feature of the structural classes concerned. The average accuracy of prediction by the current method for the 4 × 30 regular proteins is 99.2%, and that for 64 independent testing proteins not included in the training database is 95.3%. To further validate its efficiency, a jackknife analysis has been performed for the current method as well as the previous ones, and the results are also much in favor of the current method. To complete the mathematical basis, a theorem is presented and proved in Appendix A that is instructive for understanding the novel method at a deeper level. © 1995 Wiley-Liss, Inc.