Accidental degeneracy of levels is studied in the spectrum of the Hamiltonian used frequently in applications, which is a linear combination of spherical tensors rank n<or=6 invariant with respect to transformations of a cubic group. The degeneracy arises only at definite values of the Hamiltonian parameters and seems to be irrelevant with respect to increasing Hamiltonian symmetry. The basis of irreducible representations D^Gamma of the cubic group is constructed in the space of irreducible representations D^J of the SO(3) group.