For two Banach spaces
X
X
and
Y
Y
, we denote by
K
(
X
,
Y
)
K(X,Y)
(resp.
B
(
X
,
Y
)
B(X,Y)
) the space of all compact (resp. bounded) linear operators from
X
X
to
Y
Y
. In this paper, we show that for
1
≤
p
,
q
>
∞
1\leq p,q>\infty
,
K
(
ℓ
p
,
ℓ
q
)
K(\ell _{p},\ell _{q})
is an 8-Lipschitz retract of
B
(
ℓ
p
,
ℓ
q
)
B(\ell _{p},\ell _{q})
.