Connecting networks for two-dimensional beamforming matrices are discussed. They provide a suitable interconnection between the output ports of a Butler matrix and antenna array ports, transforming a square (and more generally, rectangular) lattice of beams into a triangular lattice of beams. This change in lattice improves the crossover between beams, reducing gain roll-off over the field of view for a given multiple fixed beam coverage. A general description of the concept is provided and numerical results are reported, which confirm a reduction in crossover level between 1 and 1.5 dB. The proposed solution is further validated through the design and test of a 4 × 4 open-ended waveguide array in K-band. The connecting network has a length of 70 mm, compared to 226 mm for the 2D Butler matrix, with a design frequency of 19.55 GHz. Good agreement is found between simulated and measured data. The desired triangular lattice of beams is confirmed with the measured multiple beams. This solution is of interest for multiple-beam millimeter-wave communication systems, considered for next generation of terrestrial and non-terrestrial networks.