The purpose of this presentation is to report on the development of a method and algorithm to decouple any linear system. To be specific, let A, B and C be arbitrary square matrices of the same order with at least one of the matrices, say A, being nonsingular. An invertible transformation is developed to convert A d²q/dt² + B dq/dt + Cq = f(t) into d²p/dt² + D dp/dt + Ω p = g(t) for which D, Ω are diagonal. The decoupling procedure is an extension of classical modal analysis, which is a time-honored method for decoupling linear dynamical systems that are either undamped or classically damped.