  In this paper we prove that a Finsler metrics has constant flag curvature if
and only if the curvature of the induced nonlinear connection satisfies an
algebraic identity with respect to some arbitrary second rank tensors. Such
algebraic identity appears as an obstruction to the formal integrability of
some operators in Finsler geometry, [4,7]. This algebraic characterisation for
Finsler metrics of constant flag curvature allows to provide yet another proof
for the Finslerian version of Beltrami's Theorem, [2,3].
