In this paper, an output feedback version of the modified error method is presented, for linear coupled plants. The novelty lies in the combination of a modified control function of Lyapunov with the observer backstepping technique to obtain a totally decentralized output feedback scheme. Furthermore, the design algorithm is presented in a new recursive form that goes beyond the general expressions yielded by the backstepping. The decentralization, i.e. the elimination of the cross-terms from the obtained multivariable controller, is rendered possible by a new choice of the regulated errors in the backstepping procedure. The internal stability and the tracking performances of the closed-loop system are still preserved, as long as the observer convergence is guaranteed and the H-infinity-norm of the plant interaction quotient is less than one. The developed scheme is successfully applied to the control of a rougher flotation phenomenological simulator.