2MAst HQb5 (left) and UCAC4 HQ (right) proper motions in a field centred on the globular cluster NGC 6121 (M 4). All stars within 30 arcmin from the cluster centre are plotted. In both panels, the circle marks the mean cluster motion as measured in Paper II. The radius of the circle is 15 mas/yr, corresponding to the size of our circular proper motion bins. The offset of both field and cluster stars in the right panel illustrates the regional systematic proper motion differences between the catalogues discussed in Sect. 2.3.