Machine Learning (ML) has become very popular within Data Mining (KDD) and Artificial Intelligence (AI) research and their applications. In the ML and KDD contexts, two main approaches can be used for inducing a Bayesian Network (BN) from data, namely, Conditional Independence (CI) and the Heuristic Search (HS). When a BN is induced for classification purposes (Bayesian Classifier - BC), it is possible to impose some specific constraints aiming at increasing the computational efficiency. In this paper a new CI based approach to induce BCs from data is proposed and two algorithms are presented. Such approach is based on the Markov Blanket concept in order to impose some constraints and optimize the traditional PC learning algorithm. Experiments performed with the ALARM, as well as other six UCI and three artificial domains revealed that the proposed approach tends to execute fewer comparison tests than the traditional PC. The experiments also show that the proposed algorithms produce competitive classification rates when compared with both, PC and Naive Bayes.