The conventional Multi-dimensional Bayesian Network Classifier (MBNC) requires its structure be bi-partitie. Removing this constraint can result into a new tool named General MBNC (GMBNC), and it enables us to model the underlying joint distribution more correctly. Based on iterative local search of Markov blankets, an algorithm called IPC-GMBNC was proposed to induce the exact structure of GMBNC. The proposed algorithm has good scalability because it does not need to recover the global Bayesian Network (BN) first. The experiments on samples generated from known Bayesian network structures indicate that IPC-GMBNC is effective, and it brings great reduction on computing complexity compared to global search approach, e.g. PC algorithm.