The SO(8) fermion pair model in its original version is unable to describe rigid axial rotation. Using the Hartree-Bogolyubov intrinsic state within an exact Schwinger realization of SO(8) we show that this can be remedied by introducing a cubic quadrupole interaction. Prolate and oblate minima are found and the degeneracy of the ..gamma.. band with the ground-state band is removed. The new interaction can be understood from a renormalization of the quadrupole operator. An analogy with the liquid drop model, where the quadrupole moment is expanded in the shape coordinates ..cap alpha../sub ..mu../, shows that the higher-order correction is of order 1/..cap omega...