In this note, we prove that the reducibility of analytic quasi-periodic linear systems close to constant is irrelevant to the size of the base frequencies. More precisely, we consider the quasi-periodic linear systems
\[
X
˙
=
(
A
+
B
(
θ
)
)
X
,
θ
˙
=
λ
−
1
ω
\dot {X} =(A+B(\theta ))X,\quad \dot {\theta }=\lambda ^{-1}\omega
\]
in
C
m
,
\mathbb {C}^{m},
where the matrix
A
A
is constant and
ω
\omega
is a fixed Diophantine vector,
λ
∈
R
∖
{
0
}
\lambda \in \mathbb {R}\backslash \{0\}
. We prove that the system is reducible for typical
A
A
if
B
(
θ
)
B(\theta )
is analytic and sufficiently small (depending on
A
,
ω
A, \omega
but not on
λ
\lambda
).