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We find a fiat band and a self-trapping band through the coupling of two unidirectional edge modes, which was originally achieved by Wang et al. [Phys. Rev. Lett. 100. 013905 (2008); Nature 461, 772 (2009)] in two-dimensional magneto-optical photonic crystals. We break up a square-lattice yttrium-iron-garnet photonic crystal forming a waveguide and two edges. Given a proper interval of the two edges, two unidirectional edge modes with opposite group velocity directions can be coupled. The coupling leads to a wide flat band in which the group velocity is near zero, and a self-trapping band in which light is totally localized around the source. The position of the flat band and the group velocity can be adjusted by the external magnetic field. Numerical simulations and theoretical analysis both demonstrate the two interesting band structures. [ABSTRACT FROM AUTHOR]