This paper presents an extension of the inverted decoupling approach that allows for more flexibility in choosing the transfer functions of the decoupled apparent process. In addition, the expressions of the inverted decoupling are presented for general n x n processes, highlighting that the complexity of the decoupler elements is independent of the system size. The realizability conditions are stated in order to select a proper configuration, and the different possible cases for each configuration are shown. Comparisons with other works demonstrate the effectiveness of this methodology, through the use of several simulation examples and an experimental lab process. (C) 2010 Elsevier Ltd. All rights reserved.