  We consider the Chern connection of a (conic) pseudo-Finsler manifold $(M,L)$
as a linear connection $\nabla^V$ on any open subset $\Omega\subset M$
associated to any vector field $V$ on $\Omega$ which is non-zero everywhere.
This connection is torsion-free and almost metric compatible with respect to
the fundamental tensor $g$. Then we show some properties of the curvature
tensor $R^V$ associated to $\nabla^V$ and in particular we prove that the
Jacobi operator of $R^V$ along a geodesic coincides with the one given by the
Chern curvature.
