We prove that a weighted Coxeter group
(
W
,
S
,
L
)
(W,S,L)
is bounded with
a
(
W
)
=
b
′
(
W
)
:=
max
{
L
(
u
)
,
L
(
w
s
,
t
)
∣
u
,
s
,
t
∈
S
,
|
W
s
,
t
|
>
∞
}
\mathbf {a}(W)=\mathbf {b}’(W):=\max \{L(u),L(w_{s,t})\mid u,s,t\in S,|W_{s,t}|>\infty \}
if the Coxeter graph of
W
W
is complete and
b
′
(
W
)
>
∞
\mathbf {b}’(W)>\infty
, where
W
s
,
t
W_{s,t}
is the parabolic subgroup of
W
W
generated by
s
≠
t
s\ne t
in
S
S
and
w
s
,
t
w_{s,t}
is the longest element in
W
s
,
t
W_{s,t}
whenever
W
s
,
t
W_{s,t}
is finite.