The purpose of this paper is to improve the risk management process in the quality management system of higher education, taking into account the hazardous factors that increase the probability of occurrence and severity of consequences of undesirable events, as well as favorable factors that reduce the probability of occurrence and severity of consequences of hazardous events. The basis of risk management in the quality management systems of higher education institutions is the “Bowtie” method, which involves six main steps of identifying inconsistency, determining the impact of hazardous and favorable factors according to the impact group, ranking hazardous and favorable factors, calculating risk, substantiating precautionary measures and checking calculations. To rank hazardous and favorable factors, the authors used the “Decision Making Trial and Evaluation” method (hereinafter—DE-MATEL), which is based on paired comparison and decision-making tools based on graph theory. An improved process is proposed for risk assessment, which differs from the known ones by the presence of the identification of the cause-and-effect relationship “hazard (inconsistency)-hazardous event-consequences”, identification of hazardous and favorable factors of the internal and external environment that affect the probability and/or the degree of severity of a hazardous event—the appearance of an inconsistency, which is carried out after the inconsistency has been determined; determination of causal hazardous and favorable factors by an acceptable method. Registers of inconsistencies (hazards), hazardous and favorable factors have been developed and proposed based on the requirements for accreditation of educational programs and the international standard ISO 9001:2015, which will allow, based on a risk-oriented approach, to provide a basis for setting the goals of a higher education institution under martial law in order to guarantee effective implementation of the mission and strategy. They are proposed for decision-making in the quality management systems of educational organizations on the substantiation of precautionary or corrective measures based on ranking the risks from identified inconsistencies, which are determined taking into account the impact of the entire set of identified significant hazardous and favorable factors. The value of this paper is to improve the quality risk management process in educational organizations, taking into account the impact of hazardous and favorable factors, and to develop an appropriate step-by-step algorithm of actions and a risk assessment form.