Risk matrices are used in process safety to rate and rank risks of hazardous events to help with decision making on risk reduction for processes. For example, commonly they are used in process hazard analysis to rate the risks of hazard scenarios. Flaws in their theoretical framework and mathematical inconsistencies in their use have been identified in the risk analysis literature. These flaws pose potentially serious problems for the application of risk matrices in process safety. One of the most significant flaws is the potential for risk ranking reversals wherein an incorrect assignment of a higher risk event to a lower risk level and a lower risk event to a higher risk level may occur. This article discusses the nature of the problem and describes how it can be addressed for risk matrices used in process safety. © 2015 American Institute of Chemical Engineers Process Saf Prog 35: 41–46, 2016