  We present the first search for the rare decay of $\eta^\prime$ into
$K^{\pm}\pi^{\mp}$ in $J/\psi\to\phi\eta^{\prime}$, using a sample of
$1.3\times10^{9}$ $J/\psi$ events collected with the BESIII detector. No
significant signal is observed, and the upper limit at the 90\% confidence
level for the ratio $\frac{{\cal B}(\eta^{\prime}\to K^{\pm}\pi^{\mp})}{{\cal
B}(\eta^{\prime}\to\gamma\pi^{+}\pi^{-})}$ is determined to be
$1.3\times10^{-4}$. In addition, we report the measurement of the branching
fraction of $J/\psi\to\phi\eta^{\prime}$ to be
$(5.10\pm0.03(\text{stat.})\pm0.32(\text{syst.}))\times10^{-4}$, which agrees
with previous results from BESII.
