  The Sun's axisymmetric flows, differential rotation and meridional flow,
govern the dynamics of the solar magnetic cycle and variety of methods are used
to measure these flows, each with its own strengths and weaknesses. Flow
measurements based on cross-correlating images of the surface magnetic field
have been made since the 1970s which require advanced numerical techniques that
are capable of detecting movements of less than the pixel size in images of the
Sun. We have identified several systematic errors in addition to the
center-to-limb effect that influence previous measurements of these flows and
propose numerical techniques that can minimize these errors by utilizing
measurements of displacements at several time-lags. Our analysis of
line-of-sight magnetograms from the {\em Michelson Doppler Imager} (MDI) on the
ESA/NASA {\em Solar and Heliospheric Observatory} (SOHO) and {\em Helioseismic
and Magnetic Imager} (HMI) on the NASA {\em Solar Dynamics Observatory} (SDO)
shows long-term variations in the meridional flow and differential rotation
over two sunspot cycles from 1996 to 2020. These improved measurements can
serve as vital inputs for solar dynamo and surface flux transport simulations.
