In the present paper we provide an interesting example of a non-degenerate precession possessing two distinct pairs $\left(p,f\right)$, $\left(p^{\prime },f^{\prime }\right)$ of axes of precession and figure. Thus the problem arises of the existence of classes of precessions possessing a unique axis of precession and a unique axis of figure. In the fourth section we show that the class of non-degenerate regular precessions enjoys this property.