Abstract: We have analysed the formulas of generalized Wigner-Eckart theorems in reference〔10〕 and the characteristics of the wave functions of mixed states due to mixing of aLby V_c. Four corollaries and the results associated with the corollaries are derived. The calculation of matrix elements in the mixed states,is reduced to a simple calculation of matrix elements in the unmixed states, or the calculation of all non-zero matrix elements between two octahedral field terms is reduced to a simple calculation of a matrix elements in mixed states.By using this method, these problems involved energy spectrum of dn ions in a trigonally or tetragonally distorted octahedral crystal field can be overall dealt with in detail.