Three versions of possible new Galactic coordinate systems based on modern catalogues 2MASS, SPECFIND, AKARI, WISE have been compared with the standard one. It was shown that the standard system is oriented in space with accuracy not better than several arcminutes. The comparison of the XPM and UCAC4 catalogues based on more than 40 million common stars in the Galactic coordinate system is presented. The systematic differences between positions and proper motions in 12 J-magnitude bins in the range 10.25–15.75 mag. were expressed by decompositions on the vector spherical harmonics. An analytical method to describe the magnitude equation was used. A new statistical criterion adapted to the HealPix data pixelization to determine the significance of all the accessible harmonics is proposed to extract signal from noise. It was found that the mutual orientation of the XPM and UCAC4 Galactic frames is in the range of several mas.