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One-loop $W$ boson contributions to the decay $H\rightarrow Z\gamma$ in thegeneral $R_\xi$ gauge are presented. The analytical results are expressed interms of well-known Passarino-Veltman functions which their numericalevaluations can be generated using {\tt LoopTools}. In the limit $d\rightarrow4$, we have shown that these analytical results are independent of theunphysical parameter $\xi$ and consistent with previous results. The gaugeparameter independence are also checked numerically for consistence. Ourresults are also well stable with different values of $\xi =0, 1, 100,$ and$\xi \rightarrow \infty$.

One-loop $W$ boson contributions to the decay $H\rightarrow Z\gamma$ in the general $R_\xi$ gauge