Single atom catalysts (SACs) are considered as efficient catalysts for hydrogen‐based energy conversion and storage because of their excellent catalytic performance for oxygen evolution reactions (OER) and oxygen reduction reactions (ORR). In the present work, a new concept of SACs is proposed with the capacity to form d‐p orbital hybridization. These computationally designed SACs contain a metal and non‐metal pair embedded in the N‐doped graphene framework (MX@N6). Based on the overpotential evaluation by the first principle theory calculations, CoS@N6 containing Co and S atom pair possessed a low overpotential of 0.37 V/0.29 V when used as a bifunctional ORR/OER catalyst. These overpotentials are much lower than Co@N6 without S atom. The electronic structure analysis revealed that non‐metal atoms of the catalyst can regulate the electronic structure of active metal sites and facilitate the adsorption and charge transfer between intermediates and the catalyst resulting in enhanced catalytic performance. This work demonstrates an alternative way to further improve the catalytic activity of SACs by introducing a non‐metal atom that may shed light on the rational design of advanced SACs for ORR/OER with high efficiency and stability.