Crystal structure of spinel compound CuIr$_{2}$S$_{4}$ was examined by powder X-ray diffraction for the insulating phase below the metal-insulator transition at $T_{MI}$ = 230 K. The superstructure spots are reproduced by considering the displacement of Ir atoms. A model for the ionic ordering of Ir$^{4+}$ and Ir$^{3+}$ with the same number is proposed for the insulating phase on the basis of the structural analysis. The model suggests that the structural change at $T_{MI}$ is driven by the formation Ir$^{4+}$ dimers. In addition, we found that the superstructure spots becomes significantly weak below 60 K, without any significant effects on electric and magnetic properties. Possible mechanism for the transition is discussed.
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