The coupling of plasmonic nanoparticles can strongly modify their optical properties. Here, we show that the coupling of the edges within a single rectangular particle leads to mode splitting and the formation of bonding and antibonding edge modes. We are able to unambiguously designate the modes due to the high spatial resolution of electron microscopy-based electron energy loss spectroscopy and the comparison with numerical simulations. Our results provide simple guidelines for the interpretation and the design of plasmonic mode spectra.