This paper presents theoretical investigation of the propagation of surface acoustic waves (SAWs) across the boundary between metallized (electrically shorted) and unmetallized (electrically open) regions on the surface of potassium niobate crystals. Potassium niobate is a very strong piezoelectric material and has the interesting property that only one type of SAW, namely a Rayleigh wave, can exist on unmetallized surface, where as two types of SAWs, namely Rayleigh and Bleustein-Gulyaev (BG), can exist on a metallized surface. Analysis shows that the Rayleigh wave propagates through the interface with very little change in amplitude or polarization. On the other hand, almost total reflection of the BG wave is expected. Details of the theoretical analysis and calculated results will be presented.