By analyzing the properties of the nonlinear functions used in MD5 and the differences in terms of XOR and subtraction modulo 2³², this paper proves that some sufficient conditions presented by Liang Jie and Lai Xuejia are also necessary to guarantee the differential path from the 23^rd step to the 62^nd step and give a set of necessary and sufficient conditions to guarantee the output differences of the last two steps. Then, according to the set of necessary and sufficient conditions this paper presents an improved collision attack algorithm on MD5. Finally, it analyzes the average computational complexity of the attack algorithm which is 0.718 7 times of that of the previous collision attack algorithms and proves the efficiency of the improved algorithm by computer simulations.