Decision tree algorithms, being accurate and comprehensible classifiers, have been one of the most widely used classifiers in data mining and machine learning. However, like many other classification algorithms, decision tree algorithms focus on extracting patterns with high generality and in the process, these ignore some rare but useful and interesting patterns that may exist in small disjuncts of data. Such extraordinary patterns with low support and high confidence capture very specific but exceptional behavior present in data. This paper proposes a novel Enhanced Decision Tree Algorithm for Discovering Intra and Inter-class Exceptions (EDTADE). Intra-class exceptions cover objects of unique interest within a class whereas inter-class exceptions capture rare conditions due to which we are forced shift the class of few unusual objects. For instance, whales and bats are examples of intra-class exceptions since these have unique characteristics within the class of mammals. Further, most of the birds are flying creatures, but the rare birds, like penguin and ostrich fall in the category of no flying birds. Here, penguin and ostrich are inter-class exceptions. In fact, without knowing about such exceptional patterns, our knowledge about a domain is incomplete. We have enhanced the decision tree algorithm by defining a framework for capturing intra and inter-class exceptions at leaf nodes of a decision tree. The proposed algorithm (EDTADE) is applied to many datasets from UCI Machine Learning Repository. The results show that the EDTADE has been successful in discovering many intra and inter-class exceptions. The decision tree augmented with intra and inter-class exceptions are more accurate, comprehensible as well as interesting since these provide additional knowledge in the form of exceptional patterns that deviate from the general rules discovered for classification