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A detailed investigation of the hydrodynamic stability to transverse linear disturbances of a steady, one-dimensional detonation in an ideal gas undergoing an irreversible, unimolecular reaction with an Arrhenius rate constant is conducted via a normal-mode analysis. The method of solution is an iterative shooting technique which integrates between the detonation shock and the reaction equilibrium point. Variations in the disturbance growth rates and frequencies with transverse wavenumber, together with two-dimensional neutral stability curves and boundaries for all unstable low- and higher frequency modes, are obtained for varying detonation bifurcation parameters. These include the detonation overdrive, chemical heat release and reaction activation energy. Spatial perturbation eigenfunction behaviour and phase and group velocities are also obtained for selected sets of unstable modes. Results are …