The paper numerically investigates the transmission of harmonic surface acoustic waves (SAWs) across the perfectly bonded and perfectly sliding contacts between two 90°-wedges, at least one of which possessing piezoelectric properties. The finite element method in frequency domain is used. The structures are constructed of lithium niobate, fused quartz, silicon and gallium arsenide. The SAW is always incident from lithium niobate. The dependences of the transmission coefficient on the combination of materials and the orientation of the lithium niobate, as well as on the height of the step at the interface between the two parts of the structure are computed and analyzed. This step can appear in the process of fabrication of the composite substrate. The obtained results demonstrate that SAWs are able to transmit fairly efficiently across a wedge-like contact. Therefore such structures can be useful, in particular, in cases when it is advantageous to generate a SAW in one strongly piezoelectric material and observe its action, e.g., due to the transmitted surface normal displacement in another material like in SAW-driven microfluidics.