  An associated Nijenhuis tensor of endomorphisms in the tangent bundle is
introduced. Special attention is paid to such tensors for an almost
hypercomplex structure and the metric of Hermitian-Norden type. There are
studied relations between the six associated Nijenhuis tensors as well as their
vanishing. It is given a geometric interpretation of the vanishing of these
tensors as a necessary and sufficient condition for the existence of a unique
connection with totally skew-symmetric torsion tensor. Similar idea is used in
the paper of T. Friedrich and S. Ivanov in Asian J. Math. (2002) for some other
structures. Finally, an example of a 4-dimensional manifold of the considered
type with vanishing associated Nijenhuis tensors is given.
