For hypercube networks which have faulty nodes, a few ecient dynamic routing algorithms have been proposed by allowing each node to hold the status of neighbors. We propose two improved versions of the algorithm of Chiu and Wu by using the notion of full reachability. A fully reachable node means that the node can reach all nonfaulty nodes which have Hamming distance h from the node via a path of length h. The simulation shows that the algorithms give sucient eect when they are applied to low-dimensional hypercubes.