The success of banking institution directly depends not only on the quality of provided services, but also on the reputation of bank on the market. This issue is especially acute for the bank, since its effectiveness largely depends on the behavior and degree of trust in it by customers, creditors, the state, counterparties and partners. Therefore, for the banking business, the threat of reputation loss has taken one of the first places in the list of the most significant risks. The article substantiates the theoretical and methodological principles for improving the management system of reputational risk in banking. The object of the research is the process of managing the reputational risk in banks, and the subject of the research is theoretical and methodical approaches to the management of reputational risk in banks. The study of scientific works of foreign and domestic scientists and the regulatory framework made it possible to generalize the main approaches to the interpretation of the concept of "reputational risk". It has been found that most of the authors of the considered methodical approaches concerning reputation and risk in banks do not distinguish between the concepts of "business reputation" and "reputational risk". Reputation risk is associated with the loss of business reputation, trust and loyalty to the bank on the part of customers and partners, i.e. concerns the management of relations with interested persons. It has been proven that reputation risk can arise as a result of other types of banking risks, or the appearance of such factors as information asymmetry. It has been established that the main measures to minimize the risk of loss of business reputation (reputational risk) in banks are: the implementation of an appropriate information policy, which would involve the publication of information about the bank on the bank's official website and in the mass media, aimed at maintaining the positive reputation of the bank and its image; the participation in thematic conferences, meetings and current interaction with participants of the financial market, settlement of disputed issues by clients and partners of the bank in working order.