Using a detailed kinetic model of chemical interaction, numerical investigation of influence of a preliminary preparation of a stoichiometrical hydrogen-air mixture (decomposition of some volumes of molecular hydrogen and molecular oxygen gases into atomic gases) on characteristics of a propagating detonation wave has been carried out. It has been obtained that the preliminary partial dissociation of the gas mixture results in an essential decrease of the detonation cell size and a small increase of the self-sustained detonation wave propagation velocity. Due to the established detonation combustion features, preliminary preparation of the mixture can be used to prevent destruction of a detonation wave in channels with both a single transverse barrier and a barrier domain.