We reanalyze the spectra of α Ori (M2 Iab) and μ Cep (M2 Ia) observed with the balloon-borne telescope Stratoscope II more than 35 years ago, and we confirm the presence of water in these early M supergiant stars. This identification was first proposed by the Stratoscope observers themselves (Woolf, Schwarzschild, and Rose in 1964; and Danielson, Woolf, and Gaustad in 1965), but this important discovery was overlooked for a long time without any follow-up observation. Consequently, this finding has so far had little influence on the theory of the atmosphere of red supergiant stars. A reason for this may be due to an early criticism by Wing and Spinrad, who suggested CN instead of H2O for the spectral features observed by Stratoscope II. This alternative proposition has more easily been accepted since CN has widely been observed from the Sun to red supergiants, while H2O has been observed only in very cool stars such as Mira variables. In fact, we confirm that the self-consistent photospheric model of the early M supergiants shows CN bands but no H2O band in the near-infrared. Nevertheless, we find that the contribution of CN is only minor and that H2O should be the dominant absorber for the 1.4 and 1.9 μm features on the Stratoscope spectra of α Ori and μ Cep, a conclusion opposite to that of Wing and Spinrad. The observed spectra can best be interpreted by the water gas with the column density of the order of 1020 cm-2 and temperature about 1500+/-500 K, but they cannot be originating in the photosphere. We suggest a possible presence of a gaseous component not as hot as the chromosphere but warmer than the cool expanding envelope. On the other hand, we notice that the mid-infrared pure-rotation lines of H2O recently discovered on Betelgeuse (α Ori) and Antares (α Sco) by Jennings and Sada may partly be originating in the photosphere, even though the larger part should again be nonphotospheric in origin. Thus, the presence of water possibly originating in the outer atmosphere of Betelgeuse is confirmed by the independent observation in the mid-infrared region. We now conclude that water should be an important new probe on the atmosphere of the early M supergiant stars, for which water has not been recognized as such until recently.