Abstract: For the needs of treatment of ligand field theory with molecular orbital as the starting point,the relation between the three dimensional orthogonal group O₃ and the full octahedral group O_h is discussed in detail, then the corresponding V-coupling coefficients from O₃ to O_h is defined as an extension of those coefficents from R₃ to octahedral group 0 which have been proposed by Tang et al. Under some symmetry rules, the numerical values of the coefficients from O₃ to O_h can be directly obtained from the values of the coefficients from R₃ to Owithout calculations.