  The problem of unphysical zero modes in lattice QCD with Wilson fermions can
be solved in a clean way by including a mass term proportional to $i \psibar
\gamma_5 \tau^3 \psi$ in the standard lattice theory with Nf=2 mass degenerate
Wilson quarks. We argue that up to cutoff effects, this lattice theory is
equivalent to standard lattice QCD, for suitable choices of the mass parameters
and with a natural re-interpretation of observables. On-shell O(a) improvement
can be implemented in a straightforward way.
