As a critical part of desision tree （DT） growth， its nodes can be split to grow by either axis- or non-axis-aligned way based on such splitting criteria as purity and misclassification error. However， these have nothing to do with the geometric structure of data， e.g. multicentric data or single-center data. In order to compensate for this， two splitting criteria are proposed by combining the between-class margin in the same inner node （BCM） and the between-node margin within the same class （BNM） respectively with the purity measure in weighting and the two-step method. Unlike traditional greedy growth of DT which only finds the current locally optimal splitting point， the proposed method first selects the top-k purity splitting nodes， then determines the optimal one by maximizing BCM and minimizing BNM. Since not only alleviating purity-based local optimality but also considering global structures of the data， our method greatly improves the division of descendant nodes and generalization of the formed trees， while enhancing the interpretability. In addition， two aforementioned splitting criteria can be combined to further boost the performance. The comparison results on 21 benchmark datasets show an improvement in predictive performance of new trees with reduction in complexity， while also are competitive with many other DTs using hybrid splitting criteria.