Abstract: For non--axially symmetric electric quadrupole interactions of radioactive nuclei in a polycrystallinesource, the interaction frequencies and perturbation functions for spin--four are quite different fromthose for the coventional spin--five--halves nuclei. Therefore, for understanding and analyzing PerturbedAngular Correlation (PAC) experiments that use spin--four probe nuclei, we calculated the energyeigenvalues, the eigenvectors and consequentely the perturbation functions G_(kk)(t) for η≥0, l = 4. Thenumerical results of these calculations are presented.