To elucidate the effect of structural irregularity on propagation properties of optical waves in discontinuous magneto-optical media, theoretical analysis was carried out by employing random matrix technique and a model with one-dimensional quasirandom array structure. The analysis revealed that the effect of structural irregularity was so significant that the dispersion curves of optical waves varied considerably depending on the media structures. However, no matter how the medium structure varies irregularly, dispersion curves of waves always exist within the confines between those of the half (0...01...1) and the alternate (0101...01) structures. This fact suggests that the effect of structural irregularity becomes less significant when the discontinuous media have fine discrete structures, where the dispersion curves of the half and the alternate structures are very close.