  Let $F^{2n}=(M,M',F^{\ast})$ be an even-dimensional pseudo-Finsler manifold.
We construct an almost hypercomplex structure on any chart domain of a certain
atlas of $M'$ by using a considered non-linear connection. Then by using the
almost hypercomplex structure we define two new families of Finsler
connections. Also we show that for any Finsler connection $\nabla$ there exists
a linear connection $D$ such that the local almost hypercomplex structure is
parallel with respect to it.
