Suppose H is a  Hilbert  space , and $N_0(\D)$ is the set \\

$N_0(\D)=\{f(z)=I+B(1)z+B(2)z^2+\cdots |f(z)$ is 

an analytic operator function on the open uint disk 

$\D, Ref(z)\>0$, where $ \{B(n)\}_{n=1}^{\oo}$ are 

normal operators on H,and $B_nB_m=B_mB_n$ 

for every positive integers n,m\}. \\

The note proves that Holland F's extreme point theorem 

can be generalized to\\ 

1. $N_0(\D)$  has not any strong extreme point, 

when $dimH>1$.\\

2. The sub-strong extreme points of $N_0(\D)$ have 

the following forms\\

$$f(z)=(I+Uz)(I-Uz)^{-1},z\in \D,$$

where U is an unitary operator on H.