Abstract: Based on careful analysis on the shortest path traditional approaches,a new approach of finding out unreasonable activity loops is present for improving efficiency of the traditional approaches,the approach is named as SPRM(shortest path reachable matrix).Compared with the previous approaches,SPRM introducs the"reachable matrix"into calculating the shortest path and can show activity loops and distances directly.The definition,operating rules of SPRM and others related to SPRM are described.In the end,the approach is applied to a practical process,the loops and paths are found out quickly. The approach provids a new resolution to the business process reengineering(BPR).