Triple bonding is conventionally considered to be the limit for multiply bonded main group elements, despite higher metal-metal bond orders being frequently observed for transition metals and lanthanides/actinides. Here, using high-level theoretical methods, we show that C2 and its isoelectronic molecules CN+, BN and CB- (each having eight valence electrons) are bound by a quadruple bond. The bonding comprises not only one σ- and two π-bonds, but also one weak ‘inverted’ bond, which can be characterized by the interaction of electrons in two outwardly pointing sp hybrid orbitals. A simple way of assessing the energy of the fourth bond is proposed and is found to be ~12-17 kcal mol-1 for the isoelectronic species studied, and thus stronger than a hydrogen bond. In contrast, the analogues of C2 that contain higher-row elements, such as Si2 and Ge2, exhibit only double bonding.