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Outlier detection, or detection of exceptional data, is a key element for financial databases, because the necessity of fraud prevention. Here, we propose an efficient method for this task which includes an innovative end-user explanation facility. The best design was based on an unsupervised learning schema, which uses an adaptation of the Artificial Neural Network paradigms and the Expert System shells. In our method, the cluster that contains the smaller number of instances is considered as outlier data. The method provides an explanation to the end user about why this cluster is exceptional with regard to the data universe. The proposed method has been tested and compared successfully using well-known academic data, and a real and very large financial database.