We prove the inequality
h
(
x
)
−
1
G
(
x
,
y
)
h
(
y
)
⩽
c
G
(
x
,
y
)
+
c
h{(x)^{ - 1}}G(x,y)h(y) \leqslant cG(x,y) + c
, where
G
G
is the Green function of a plane domain
D
,
h
D,\;h
is positive and harmonic on
D
D
, and
c
c
is a constant whose value depends on the topological nature of the domain. In particular, for the class of proper simply connected domains
c
c
may be taken to be an absolute constant. As an application, we prove the Conditional Gauge Theorem for plane domains of finite area for which the constant
c
c
in the above inequality is finite.