Automated text categorization is attractive because it frees organizations from the need of manually organizing document bases. Support Vector Machine (SVM) is an efficient technique for text categorization. Computing kernel matrix is the key in text categorization with SVM. When the kind of texts is large, the matrix of texts will become sparse. If we compute the kernel matrix directly, it will waste much time and memory space. To save time, the paper explored the hash function in the process of computing the kernel matrix. Then we propose an improved algorithm for multiclass text categorization. The paper also gives the good property of the improved algorithm from the theoretical and experimental aspects. We compared the improved algorithm with the original algorithm. Experiment shows that the improved algorithm can save much computational time.