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This theoretical work demonstrates that as many as thirty two new shearhorizontal (SH) acoustic waves can propagate in the piezoelectromagnetic transversely isotropic (class 6 mm) plates. These theoretical investigations relate to the homogeneous boundary conditions when the same set of the mechanical, electrical, and magnetic boundary conditions are applied to the upper and lower free surfaces of the piezoelectromagnetic plate. These new dispersive SHwaves propagating in the piezoelectromagnetic plate can have an infinite number of modes when the phase velocity Vph is larger than the speed Vtem of the bulk acoustic SHwave in the plate. For Vph
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