  Four of nine exoplanets found by microlensing were detected by the resonant
caustic, which represents the merging of the planetary and central caustics at
the position when the projected separation of a host star and a bounded planet
is s~1. One of the resonant caustic lensing events, OGLE-2005-BLG-169, was a
caustic-crossing high-magnification event with $A_{max} \sim$ 800 and the
source star was much smaller than the caustic, nevertheless the perturbation
was not obviously apparent on the light curve of the event. In this paper, we
investigate the perturbation pattern of the resonant caustic to understand why
the perturbations induced by the caustic do not leave strong traces on the
light curves of high-magnification events despite a small source/caustic size
ratio. From this study, we find that the regions with
small-magnification-excess around the center of the resonant caustic are rather
widely formed, and the event passing the small-excess region produces a
high-magnification event with a weak perturbation that is small relative to the
amplification caused by the star and thus does not noticeably appear on the
light curve of the event. We also find that the positive excess of the inside
edge of the resonant caustic and the negative excess inside the caustic become
stronger and wider as $q$ increases, and thus the resonant caustic-crossing
high-magnification events with the weak perturbation occur in the range of $q
\leqslant 10^{-4}$. We determine the probability of the occurrence of events
with the small excess $|\epsilon| \leqslant 3 %$ in high-magnification events
induced by a resonant caustic. As a result, we find that for the Earth-mass
planets with a separation of ~ 2.5 AU, the resonant caustic high-magnification
events with the weak perturbation can occur with a significant frequency.
