We propose a new process for the generation of the 2-day wave near the stratopause. It is shown that the simultaneous fulfillment of the conditions of barotropic and inertial instability leads to a new mode class that includes the 2-day wave. The mixing of both instabilities leads to high growth rates. The stability calculations use the latitudinally dependent zonal-mean zonal wind in the stratopause region. Wind profiles of the stratopause region were taken from the U.K. Met Office reanalyses for time periods with and without observed 2-day waves. For the Southern Hemisphere summer the calculations yield westward propagating waves with a 2-day period at m = 3 and m = 4 and e-folding times reaching 2.5 days when a so-called mixed barotropic-inertial instability is present. When this is not the case, the instability calculation does not yield the 2-day wave, which then is not present in the observations. This mixed instability can lead to e-folding times shorter than possible for pure barotropic instability. We used idealized zonal wind profiles for sensitivity studies on the instability criteria. The wind profiles model the wind conditions during various observed 2-day wave bursts. The 2-day wave period and growth rate are shown to be strongly dependent on the inertial instability parameter, as well as on the meridional extent of the region with negative vorticity gradient. This might also explain why the 2-day wave occurs as bursts. The growth rates at wave numbers m = 3 and 4 maximize at different values of the Lamb parameter, which is a measure for the vertical wavelength.