Abstract—The PPMXL and UCAC4 catalogs are compared by representing the differences between the positions and proper motions of stars as decompositions into a set of orthogonal vector harmonics withallowancemade for themagnitude equation. A list of 41 316 676 common stars has been compiled using the star identification procedure in the J band (2MASS photometric system). The mean differences betweenthe stellar positions and proper motions have been referred to the centers of 1200 ealPix pixels on the sphere. These data have been generated in the equatorial coordinate system for the stars belonging to 12 J magnitude bins with a width of 0.5m for mean values from 10m. 25 to 15m. 75. For each sample of stars, the differences have been approximated by vector spherical harmonics. A new statistical criterion that is oriented to using HealPix data pixelization and that allows the significance of all the ccessible harmonics to be determined is proposed to extract the signal from noise. An analytical method that includ