Let
A
,
B
A,B
be unital
C
∗
C^*
-algebras and
P
∞
(
A
,
B
)
P_\infty (A,B)
be the set of all completely positive linear maps of
A
A
into
B
B
. In this article we characterize the extreme elements in
P
∞
(
A
,
B
,
p
)
P_\infty (A,B,p)
,
p
=
Φ
(
1
)
p=\Phi (1)
for all
Φ
∈
P
∞
(
A
,
B
,
p
)
\Phi \in P_\infty (A,B,p)
, and pure elements in
P
∞
(
A
,
B
)
P_\infty (A,B)
in terms of a self-dual Hilbert module structure induced by each
Φ
\Phi
in
P
∞
(
A
,
B
)
P_\infty (A,B)
. Let
P
∞
(
B
(
H
)
)
R
P_\infty (B(H))_R
be the subset of
P
∞
(
B
(
H
)
,
B
(
H
)
)
P_\infty (B(H), B(H))
consisting of
R
R
-module maps for a von Neumann algebra
R
⊆
B
(
H
)
R\subseteq B(\mathbb {H})
. We characterize normal elements in
P
∞
(
B
(
H
)
)
R
P_\infty (B(H))_R
to be extreme. Results here generalize various earlier results by Choi, Paschke and Lin.