  A few years ago some attention has been given to a fermionic action on the
lattice, with a Wilson-like term which is chirally invariant but breaks the
hypercubic space-time lattice symmetry. This action describes two Dirac fields
in the continuum limit, provided the coefficient $\lambda$ of the Wilson-like
term satisfies $\lambda > \frac{1}{2}$. In this letter it is shown that for
$\frac{1}{2} < \lambda \leq 1$ the theory is link-reflection positive. The
propagator has the expected real energy poles. Modulo a phase shift on the
fermions, the only relevant terms which can be added to the action respecting
its symmetries have dimension $4$.
