Hyper-sphere support vector machines are proposed for solving multi-class classification problem. How to correctly classify the intersections of hyper-spheres is important for sphere structure support vector machines. Based on the analysis of such data samples, this paper presents a new simple classification rule which leads to a better generalization accuracy than the existing sub-hyper- sphere SVMs. Experimental results show our method is feasible and improves the performance of the resulting minimum bounding sphere-based classifier.