Abstract: A new method based on angular momentum theory was proposed to construct the basis functions of the irreducible representations(IRs) of point groups. The transformation coefficients, i. e. , coefficients S, are the components of the eigenvectors of some Hermitian matrices, and can be made as real numbers for all pure rotation point groups. The general formula for coefficient S was deduced, and applied to constructing the basis functions of single-valued irreducible representations of icosahedral group from the spherical harmonics with angular momentum j≤7.

Key words: Irreducible representation, Basis function, I group, Angular momentum