  We present the ground state pairing correlations in the $S_4$ symmetric
microscopic model for iron-based superconductors, computed with the
constrained-path Monte Carlo method. For various electron fillings and
interaction strengths, we find that the $s_{xy}$ pairing dominates over other
pairing correlations and is positive when the pair separation exceeds several
lattice constants, whatever for iron pnictides and iron chlcogenides. These
ground state properties, especially the long range part pairing correlations
re-confirm the previous finite temperature results published in Phys. Rev.
Lett. 110, 107002(2013). We further our study by including the nearest
neighbour interaction $V$ and it is found that the $s_{xy}$ pairing correlation
is slightly suppressed by the increasing $V$.
