We show that the Glover-Doyle algorithm can be formulated simply by using the (J,J’)-lossless factorization method and chain scattering matrix description. This algorithm was first stated by Glover and Doyle in 1988. Because the corresponding diagonal block of the (J,J’)lossless matrix in the general 4-block H-infinity control problem of the Glover-Doyle algorithm is not square, a new type of chain scattering matrix description is developed. With this description in hand, we obtain two types of state-space solution, which are similar to each other. Thus a similarity transformation between these solutions in the 4-block H-infinity control problem can also be obtained. The main idea of the solution is illustrated by means of block diagrams.