  We discuss the naive lattice fermion without the issue of doublers. A local
lattice massless fermion action with chiral symmetry and hermiticity cannot
avoid the doubling problem from the Nielsen-Ninomiya theorem. Here we adopt the
forward finite-difference deforming the $\gamma_5$-hermiticity but preserving
the continuum chiral-symmetry. The lattice momentum is not hermitian without
the continuum limit now. We demonstrate that there is no doubling issue from an
exact solution. The propagator only has one pole in the first-order accuracy.
Therefore, it is hard to know the avoiding due to the non-hermiticity. For the
second-order, the lattice propagator has two poles as before. This case also
does not suffer from the doubling problem. Hence separating the forward
derivative from the backward one evades the doublers under the field theory
limit. Simultaneously, it is equivalent to breaking the hermiticity. In the
end, we discuss the topological charge and also demonstrate the numerical
implementation of the Hybrid Monte Carlo.
