To investigate the origin of the instability of the water network consisting of a specific (so-called antimagic) number of molecules, we report infrared spectra of cold protonated water clusters H⁺(H₂O)_n (n = 20-23) tagged with weakly bound H₂ molecules. In this size range, only in n = 22, which has been known to be an antimagic number cluster, is a band attributed to the one-coordinated, dangling water molecule observed. This observation indicates that the 22nd water molecule is loosely bound to the surface of the closed cage structure of H⁺(H₂O)₂₁. This band has been missing in any spectra of the warmer and bare cluster of n = 22. The present results evidence the characteristic cluster structure of the antimagic numbered cluster, which has been predicted by Singh et al. (Angew. Chem., Int. Ed. 2006, 45, 3795) and suggests that the thermal and dynamic effects perturb the spectrum, structure, or both in warmer cases.