In the three-stage rearrangeable switch-ing network, an internal blocking can occur. However, such a blocking can be eliminated by rearranging the already set-up paths, and thus the network can satisfy any connection requirement. To eliminate this internal blocking, a successive rearrangement of more than one already set-up path is required. The sequence of the paths to be rearranged can clearly be represented by extending the notion of the connection chain introduced by Gotoh. This paper presents a sufficient condition for the Internal blocking to be eliminated by the rearrangement in the extended connection chain, which is a basis for the rearrangement algorithm. It is also verified that the rearrangement algorithm proposed by Gotoh satisfies the sufficient condition. Based on these results, a connection chain is shown in which the internal blocking can be eliminated by the rearrangement. The algorithm to search for the connection chain and to perform the rearrangement is presented. Compared with past methods, in the proposed method, a fewer number of paths is distorted. The usefulness of the method is examined by a simulation.