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Localized bending waves in a thin elastic orthotropic cantilever plate reinforced by a rigid rib are studied. A condition under which the edge waves can be eliminated is determined. The condition requires that the rib have a certain minimal stiffness. Such waves are time-varying, and have spatially nonuniform bending perturbations that are localized in the proximity of free surface and are quickly decaying to zero. A general solution is presented and the particular case of an isotropic reinforced plate is shown. An inverse method is described for identifying the elastic properties of the rib.