In the chain scattering framework, it has been shown in Lee and Soh ( 2004) that the problem of simultaneous H-infinity stabilization of a finite collection of l linear time-invariant plants such that each closed-loop transfer function has an H-infinity norm less than a prescribed performance level is equivalent to a simultaneous strongly H-infinity stabilizing problem, i.e. finding a single stable and norm bounded controller for associated l-1 unimodular plants such that each resulting closed-loop system is stable and norm bounded. This paper attempts to provide a solution to the simultaneous strongly H-infinity stabilization problem. A new sufficient condition in the form of the solution to only one algebraic Riccati equation is provided for the existence of a strongly stabilizing H-infinity controller for a given stable system obtained from the parameterization of stabilizing H-infinity controllers. With the parameterization of strongly stabilizing H-infinity controllers provided in this paper, a solution is given for the simultaneous strongly H-infinity stabilization problem and hence, a methodology for the synthesis of a common controller for the simultaneous H-infinity stabilization of more than two plants is developed. A numerical example for the simultaneous H-infinity stabilization of three plants is given to illustrate our results.