Abstract: A few rare earth compounds have the structure of point group Dn symmetry. The link-up of the group chain from SO(3)to D_n is a matter of importance. In this paper, theoretical method of the Ligand Field theory proposed by Tang and his coworkers is used as a startling point. The transformation propety of SO(3)-D_n, is discussed. The concept of the characteristic Mof the irreducible representation of Dn is introduced. The phase factors [-1]^Γ, [-1]^γ the V-coefficients, the symmetrized [Γ²] and anisymmetrized (Γ²) squares of irreducible representation, factors(-1)^Γ, θ(Γ_MΓ_MΓ_M) for D_n and S_mFrⁱ parameter of SO(3)-D_n are given.