The propagation of edge localized spin waves (E-SWs) in yttrium iron garnet (YIG) microstripes with/without the proximate magnetic microstructures is investigated by micromagnetic simulations. A splitting of the dispersion curve with the presence of permalloy (Py) stripe is also observed. The E-SWs on the two edges of YIG stripe have different wavelengths, group velocities, and decay lengths at the same frequencies. The role of the Py stripe was found to be the source of the inhomogeneous static dipolar field without dynamic coupling with YIG. This work opens new perspectives for the design of innovative SW interference-based logic devices.