  We develop a new interpolation scheme, based on harmonic inpainting, for
reconstructing the cosmic microwave background temperature data within the
Galaxy mask from the data outside the mask. We find that, for scale-invariant
isotropic random Gaussian fluctuations, the developed algorithm reduces the
errors in the reconstructed map for the odd-parity modes significantly for
azimuthally symmetric masks with constant galactic latitudes. For a more
realistic Galaxy mask, we find a modest improvement in the even-parity modes as
well.
