We consider the spherical complementary series of rank one Lie groups $$H_n={ SO }_0(n, 1; {\mathbb {F}})$$ H n = S O 0 ( n , 1 ; F ) for $${\mathbb {F}}={\mathbb {R}}, {\mathbb {C}}, {\mathbb {H}}$$ F = R , C , H . We prove that there exist finitely many discrete components in its restriction under the subgroup $$H_{n-1}={ SO }_0(n-1, 1; {\mathbb {F}})$$ H n - 1 = S O 0 ( n - 1 , 1 ; F ) . This is proved by imbedding the complementary series into analytic continuation of holomorphic discrete series of $$G_n=SU(n, 1)$$ G n = S U ( n , 1 ) , $$SU(n, 1)\times SU(n, 1)$$ S U ( n , 1 ) × S U ( n , 1 ) and SU(2n, 2) and by the branching of holomorphic representations under the corresponding subgroup $$G_{n-1}$$ G n - 1 .