A 28 GHz four-beam antenna based on the combination of a 4×4 Butler matrix and a Fabry-Perot superlayer is the final goal of this work. The matrix is designed in the low loss inverted microstrip gap waveguide technology, including the design of a transition to microstrip to enable measurements. Multibeam antennas with high efficiency are of interest for the future 5G communication systems to be used for instance in MIMO systems.