  By following the Foldy-Wouthuysen (FW) transformation of the Dirac equation,
we work out the exact analytic expressions up to the $1/M^4$ order for the
general cases in the covariant density functional theory. These results are
further compared with the corresponding ones derived from another novel
non-relativistic expansion method, the similarity renormalization group (SRG).
Based on that, the origin of the difference between the results obtained by the
FW transformation and SRG method is explored.
