  A role of the multipole interaction in the description of the $\triangle I$=4
staggering phenomenon is investigated in a model consisting of a single-$j$
shell filled by identical nucleons. Exact diagonalization of the
quadrupole-plus-hexadecapole Hamiltonian shows that the
hexadecapole-hexadecapole interaction can produce a $\triangle I$=4 periodicity
in the yrast sequence.
