We study theoretically the effect of second-order coupling (SOC) on the tunneling dynamics in a planar four-well system with only one well periodically modulated.We find that SOC between next-nearest neighboring wells facilitates localization.Due to SOC,the suppression of tunneling occurs over a finite range of parameters,in stark contrast to the normal coherent destruction of tunneling in the nearest-neighbor tight-binding approximation.This counter-intuitive phenomenon of SOC-enhanced localization can be attributed to the existence of a localized Floquet state rather than the degeneracy of quasi-energy levels in such a system.