This work presents a new general purpose classifier named Averaged Extended Tree Augmented Naive Bayes (AETAN), which is based on combining the advantageous characteristics of Extended Tree Augmented Naive Bayes (ETAN) and Averaged One-Dependence Estimator (AODE) classifiers. We describe the main properties of the approach and algorithms for learning it, along with an analysis of its computational time complexity. Empirical results with numerous data sets indicate that the new approach is superior to ETAN and AODE in terms of both zero-one classification accuracy and log loss. It also compares favourably against weighted AODE and hidden Naive Bayes. The learning phase of the new approach is slower than that of its competitors, while the time complexity for the testing phase is similar. Such characteristics suggest that the new classifier is ideal in scenarios where online learning is not required.