  It's pointed out that the values of the generators derived by the modern
gyrokinetic theory are inappropriately amplified by the pullback transform with
the existence of electromagnetic perturbation, and the trajectory equations of
the gyrocenter include terms containing the perturbative magnetic vector
potential not in the form of its curl. These terms are not physical ones, as
the perturbative magnetic vector potential could include an arbitrary gauge
term. In this paper, instead of the single-parameter Lie transform method
utilized by the modern gyrokinetic theory, a multi-parameter Lie transform
method is utilized. All characteristic scales of the system can be taken into
account. With the assistance of a kind of linear cancellation rule, the new
method can decouple the gyroangle $\theta$ from the remaining degrees of
freedom up to the second order of the parameter as the ratio between the Larmor
radius and the transverse length scale of the equilibrium magnetic field. With
this new method, those nonphysical terms don't appear anymore in the trajectory
equations.
