We analyze the longitude-velocity diagram (LVD) of 12CO line emission from archival data and use the most accurate rotation curve (RC) of the Milky Way to transform radial velocity to face-on position in the galactic plane. We find that, especially in the inner Milky Way, the face-on transformation is highly sensitive to the adopted RC in the sense that deviations of the RC from the true rotation velocity lead to artifact holes or overcrowded concentrations along the tangent circle for overestimated or underestimated RC, respectively. Even if the RC is sufficiently accurate, non-circular motion such as with the 3 kpc expanding ring introduces significant artifacts in the resulting face-on-map, as long as a circular rotation is assumed. On the other hand, if we properly take into account the non-circular motion, it can be used to solve the near-far degeneracy problem of determination of kinematic distance. We thus propose a new method to solve the degeneracy problem by incorporating the expanding motion of a ring. We apply the method to the LVD of the 3-kpc expanding ring and present a face-on map projected onto the galactic plane for the first time.