Bayesian classifiers such as Naive Bayes or Tree Augmented Naive Bayes (TAN) have shown excellent performance given their simplicity and heavy underlying independence assumptions. In this paper we introduce a classifier taking as basis the TAN model and taking into account uncertainty in model selection. To do this we introduce decomposable distributions over TANs and show that they allow the expression resulting from the Bayesian model averaging of TAN models to be integrated into closed form. With this result we construct a classifier with a shorter learning time and a longer classiffication time than TAN. Empirical results show that the classifier is, most of the cases, more accurate than TAN and approximates better the class probabilities.