The atomic layer of hybridized hexagonal boron nitride (h-BN) and graphene has attracted a great deal of attention after the pioneering work of P. M. Ajayan et al. on Cu foils because of their unusual electronic properties (Ci, L. J.; et al. Nat. Mater. 2010, 9, 430-435). However, many fundamental issues are still not clear, including the in-plane atomic continuity as well as the edge type at the boundary of hybridized h-BN and graphene domains. To clarify these issues, we have successfully grown a perfect single-layer h-BN-graphene (BNC) patchwork on a selected Rh(111) substrate, via a two-step patching growth approach. With the ideal sample, we convinced that at the in-plane linking interface, graphene and h-BN can be linked perfectly at an atomic scale. More importantly, we found that zigzag linking edges were preferably formed, as demonstrated by atomic-scale scanning tunneling microscopy images, which was also theoretically verified using density functional theory calculations. We believe the experimental and theoretical works are of particular importance to obtain a fundamental understanding of the BNC hybrid and to establish a deliberate structural control targeting high-performance electronic and spintronic devices.