  The presence of astrophysical emissions between the last scattering surface
and our vantage point requires us to apply a foreground mask on CMB sky map,
leading to large cut around the Galactic equator and numerous holes. Since many
CMB analyses, including non-Gaussianity study may be performed on a whole sky
map in a more straightforward and reliable manner, it is of utmost importance
to develop an efficient method to in-paint the CMB sky map, while still
preserving statistical properties. In this letter, we consider Monte-Carlo
simulation of constrained Gaussian field and derive it for CMB anisotropy in
harmonic space, where a feasible implementation is possible with good
approximation. We applied our method to the simulated data, which confirms the
masked area is in-painted in a way compliant with the expected statistical
properties. Subsequently, we applied our method to the WMAP foreground-reduced
maps and investigated the anomalous alignment between quadrupole and octupole
components. From our investigation, we find the alignment in the
foreground-reduced maps is even higher than the ILC map. In particular, we find
the highest alignment in the V band map, which has less foreground
contamination than other bands. Therefore, we find it hard to attribute the
alignment to residual foregrounds. Our method will be complementary to other
efforts on in-painting or reconstructing the masked CMB data, and of great use
to Planck surveyor and future missions.
