The hydrodynamic instability of the zonally averaged circulation of the atmosphere is investigated using a primitive equation model on a global domain. The classical baroclinically unstable modes are examined and a new mode of instability is found. This mode has phase-speed greater than the maximum zonal flow velocity (such a solution is impossible within the frame-work of quasi-geostrophic theory). It draws energy from the mean flow in the troposphere through baroclinic conversion and it penetrates deeply into the middle atmosphere, its growth there being a supported by convergence of vertical wave energy flux. With zonal wavenumber one it has a period of two days and an e-folding time of six days. Such instabilities may play an important role in the dynamics of the middle atmosphere.