In [1] we have obtained the following result: Let
D
D
be a bounded domain in
C
n
{{\text {C}}^n}
. Suppose there is a compact subset
K
K
of
D
D
such that for every
x
ϵ
D
x\epsilon D
there is an analytic automorphism
f
ϵ
Aut
(
D
)
f\epsilon \operatorname {Aut} (D)
and a point
a
ϵ
K
a\epsilon K
such that
f
(
x
)
=
a
f(x) = a
. Then
D
D
is a domain of bounded holomorphy, in the sense that
D
D
is the maximal domain on which every bounded holomorphic function on
D
D
can be continued holomorphically (cf. Narasimhan [2, Proposition 7, p. 127]). Here we shall give a stronger result: Under the same assumptions,
D
D
is
c
c
-complete. We note that a
c
c
-complete domain is a domain of bounded holomorphy, in particular, a domain of holomorphy. A domain of bounded holomorphy, however, need not be
c
c
-complete.