In this paper I study the extent to which the nexus between concentration and interbank linkages affects financial stability, using data for a sample of 19,689 banks in 69 countries from 1995 to 2014. I find that high levels of interbank exposures decrease the probability of observing a systemic banking crisis, when the banking system is either highly concentrated or fragmented. The relationship between concentration and stability is found to be non-monotonic, as predicted by Martinez-Miera & Repullo (2010), although not U-shaped.