Both WMAP and Planck data show a significant odd-multipole preference in the large scales of the cosmic microwave background (CMB) temperature anisotropies. If this pattern originates from cosmological effects, then it can be considered a crucial clue for a violation in the cosmological principle. By defining various direction dependent statistics in the full-sky Planck 2015 maps (see, for instance, Naselsky et al. (2012); W. Zhao (2014)), we found that the CMB parity asymmetry has a preferred direction, which is independent of the choices of the statistics. In particular, this preferred axis is strongly aligned with those in the CMB quadrupole and octopole, as well as that in the CMB kinematic dipole, which hints to their non-cosmological origin. In realistic observations, the foreground residuals are inevitable, and should be properly masked out in order to avoid possible misinterpretation of the results. In this paper, we extend our previous analyses to the masked Planck 2015 data. By defining a similar direction dependent statistic in the masked map, we find a preferred direction of the CMB parity asymmetry, in which the axis also coincides with that found in the full-sky analysis. Therefore, our conclusions on the CMB parity violation and its directional properties are confirmed.