  We consider spherical principal series representations of the semisimple Lie
group of rank one $G=SO(n, 1; \mathbb K)$, $\mathbb K=\br, \bc, \bh$. There is
a family of unitarizable representations $\pi_{\nu}$ of $G$ for $\nu$ in an
interval on $\mathbb R^+$, the so-called complementary series, and subquotient
or subrepresentations of $G$ for $\nu$ being negative integers. We consider the
restriction of $(\pi_{\nu}, G)$ under the subgroup $H=SO(n-1, 1; \mathbb K)$.
We prove the appearing of discrete components. The corresponding results for
the exceptional Lie group $F_{4(-20)}$ and its subgroup $Spin(8,1)$ are also
obtained.
