Two additional postulates of the eightfold way are suggested on the basis of the analysis of experiments: (1) The nonlinear contribution of the isospin T and the hyper-charge Y to the mass-splitting is independent of the spin-parity of multiplets; (2) In all cases where the octet-singlet mixing takes place, nine particles are grouped into a reducible nine-dimensional representation and are represented by a 3×3 matrix. The trace of this matrix appears neither in the zeroth order term of the mass relation nor in the production and decay interactions of particles. On the basis of these postulates, the classification of the strongly interacting particles, especially the classification of the scalar mesons and the baryon resonances with higher spins, is further discussed. Some predictions are obtained and compared with experiments. The predictions of scalar mesons are discussed in detail and are compatible with experiments. Finally, the results and the implications of the classification are discussed.