  A new form of two-photon exchange(TPE) effect is studied to explain the
discrepancy between unpolarized and polarized experimental data in elastic $ep$
scattering. The mechanism is based on a simple idea that apart from the usual
TPE effects from box and crossed-box diagrams, the mesons may also be exchanged
in elastic $ep$ scattering by two-photon coupling at loop level. The detailed
study shows such contributions to reduced unpolarized cross section
($\sigma_{un}$) and polarized observables ($P_t,P_l$) at fixed $Q^2$ are only
dependent on proton's electromagnetic form factors $G_{E,M}$ and a new unknown
universal parameter $g$. After combining this contribution with the usual TPE
contributions from box and crossed-box diagrams, the ratio $\mu_pG_E/G_M$
extracted from the recent precise unpolarized and polarized experimental data
can be described consistently.
