We consider multiclass classification problems in which the set of labels are organized hierarchically as a category tree, and the examples are classified recursively from the root to the leaves. We propose a hierarchical support-vector-machine that encourages the classifiers at each node of the tree to be different from the classifiers at its ancestors. More specifically, we introduce regularizations that force the normal vector of the classifying hyperplane at each node of the tree to be orthogonal to those at its ancestors as much as possible. We establish sufficient conditions under which such an objective is a convex function of the normal vectors. We also present an efficient dual-averaging method for solving the resulting nonsmooth convex optimization problem. We evaluate the method on a number of real-world text categorization tasks and obtain state-of-the-art performance.