The Schur complex
L
λ
/
μ
ϕ
{{\mathbf {L}}_{\lambda /\mu }}\phi
has proved useful in studying resolutions of determinantal ideals, both in characteristic zero and in a characteristic-free setting. We show here that in every characteristic,
L
λ
/
μ
ϕ
{{\mathbf {L}}_{\lambda /\mu }}\phi
is isomorphic, up to a filtration, to a sum of Schur complexes
∑
ν
γ
(
λ
/
μ
;
ν
)
L
ν
ϕ
\sum \nolimits _\nu {\gamma (\lambda /\mu ;\nu ){{\mathbf {L}}_\nu }\phi }
, where
γ
(
λ
/
μ
;
ν
)
\gamma (\lambda /\mu ;\nu )
is the usual Littlewood-Richardson coefficient. This generalizes a well-known direct sum decomposition of
L
λ
/
μ
ϕ
{{\mathbf {L}}_{\lambda /\mu }}\phi
in characteristic zero.