In the decentralized strong stabilization problem for linear time-invariant finite-dimensional systems, the objective is to stabilize a given plant using a stable decentralized controller. A solvability condition for this problem is given in terms of a parity interlacing property which is to be satisfied among the real unstable poles and real unstable decentralized blocking zeros of the plant. The problem of synthesizing decentralized stabilizing controllers with minimum number of unstable poles is also solved.