Proper motions of M31 and M33 in the heliocentric reference frame. Left-hand panel: results for M31. The black pentagon represents a strictly radial motion in the galactic reference frame. The yellow dot is the weighted average of the three HST fields corrected for the internal kinematics of M31 (Sohn et al. 2012; van der Marel et al. 2012b). The black dot is the proper motion result based on the DR2 (van der Marel et al. 2019). The blue and red dots are the values derived by Salomon et al. (2021), while the diamonds and squares in different shades of blue and red are the results from this paper using DR3 and DR2, respectively. For our study, the solid error bars represent the statistical uncertainty and the dashed ones the systematic uncertainties. Right-hand panel: results for M33. The orange dot is the water maser weighted average of Brunthaler et al. (2005). The rest of the symbols are the same as in the left-hand panel.