The so-called H$alpha$ third emission occurs around pulsation phase $varphi$=0.30. It has been observed for the first time in 2011 in some RR Lyrae stars. The emission intensity is very weak, and its profile is a tiny persistent hump in the red side-line profile. We report the first observation of the H$alpha$ third emission in RR Lyr itself (HD 182989), the brightest RR Lyrae star in the sky. New spectra were collected in 2013-2014 with the Aurelie}spectrograph (resolving power R=22$,$700, T152, Observatoire de Haute-Provence, France) and in 2016-2017 with the eShel spectrograph (R=11$,$000, T035, Observatoire de Chelles, France). In addition, observations obtained in 1997 with the Elodie spectrograph (R=42$,$000, T193, Observatoire de Haute-Provence, France) were reanalyzed. The H$alpha$ third emission is clearly detected in the pulsation phase interval $varphi$=0.188-0.407, that is, during about 20% of the period. Its maximum flux with respect to the continuum is about 13%. The presence of this third emission and its strength both seem to depend only marginally on the Blazhko phase. The physical origin of the emission is probably due to the infalling motion of the highest atmospheric layers, which compresses and heats the gas that is located immediately above the rising shock wave. The infalling velocity of the hot compressed region is supersonic, almost 50 km$cdot$s$^{-1}$, while the shock velocity may be much lower in these pulsation phases. When the H$alpha$ third emission appears, the shock is certainly no longer radiative because its intensity is not sufficient to produce a blueshifted emission component within the H$alpha$ profile. At phase $varphi$=0.40, the shock wave is certainly close to its complete dissipation in the atmosphere.
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