  For the stationary Wigner equation with inflow boundary conditions, its
numerical convergence with respect to the velocity mesh size are deteriorated
due to the singularity at velocity zero. In this paper, using the fact that the
solution of the stationary Wigner equation is subject to an algebraic
constraint, we prove that the Wigner equation can be written into a form with a
bounded operator $\mathcal{B}[V]$, which is equivalent to the operator
$\mathcal{A}[V]=\Theta[V]/v$ in the original Wigner equation under some
conditions. Then the discrete operators discretizing $\mathcal{B}[V]$ are
proved to be uniformly bounded with respect to the mesh size. Based on the
therectical findings, a signularity-free numerical method is proposed.
Numerical reuslts are proivded to show our improved numerical scheme performs
much better in numerical convergence than the original scheme based on
discretizing $\mathcal{A}[V]$.
