  It is pointed out that the conventional Lie transform perturbation theory for
the guiding center motion of charged particles in a magnetic field needs to be
modified for ordering inconsistency. There are two reasons. First, the ordering
difference between the temporal variation of gyrophase and that of the other
phase space coordinates needs to be taken into account. Second, it is also
important to note that the parametric limit of the derivative of a function is
not equivalent to the derivative of the limit function. When these facts are
taken into account, the near identity transformation rule for one form related
to the Lagrangian is modified. With the modified near identity transformation
rule, the drift motion of charged particles can be described in the first
order, instead of in the second order and beyond through a tedious expansion
process as in the conventional formulation. This resolves the discrepancy
between the direct and Lie transform treatments in the Lagrangian perturbation
theory for charged particle motion in a magnetic field.
