While traditional downloading programs usually select one mirror server for retrieving a file, it is more effective to select several mirror servers and to fetch different parts of the same file from the servers in parallel from the viewpoints of downloading time and fault-tolerance of network service. We have already proposed an adaptive parallel downloading method that enables us to stabilize and accelerate the downloading time even if the network offers a wide variety of bandwidths. This paper describes a new adaptive block requesting method which improves our original method. The new method has the following features: (1) suitable parameters based on a theoretical model and (2) introduction of changing servers. Practical evaluations that focus on downloading speed and stability of downloading time confirm that the improved method is more effective than the original method.