With the advent of data warehouses and OLAP-technology, and subsequently many other systems that output information for decision-making, all such systems began to be referred to as decision support system (DSS). Thus, the original purpose of DSS has been forgotten: the selection of an effective solution from the set of possible alternatives for poorly structured or unstructured management decision-making tasks based on mathematical methods and information technology. Therefore, it would be more correct to call systems of this class Unstructured decision-making support systems (UDMSS), and other support systems, DSS. Currently, new terms are appearing, the purpose of which is to combine DSS into certain classes; for example, System DSS, Business DSS and Intelligent DSS. Research objective is the following: to develop a new UDMSS that combines elements of expert systems, data warehouses, group DMSS, author's UDMSS, and can be called Expert UDMSS (EUDMSS). The following main results are presented in the article: features of an expert unstructured decision making support system; system architecture; decisionmaking method selection module (expert system shell); decision-making module, including 50 mathematical methods (decision-making methods using the majority principle, Pareto and Bayes principle, in partial and full uncertainty, in dynamic formulation, vector optimization, methods combining various principles of matching evaluations of alternatives and other methods); system functionality.