Systems with more than one control loop are known as (MIMO), or multivariable systems. These systems are characterized by significant interactions between their inputs and outputs. Loop interactions call cause system instability. The problem of interaction can be alleviated by a proper choice of input-output pairings such that interactions will be minimized, this lead to input-output multi-variable system pairing, and development decoupling compensator unit. In this paper a generalized decoupling technique is proposed. The proposed technique uses relative gain array (RGA) to select proper pairing and hybrid genetic and nelder-mead algorithm (HGNMA) to estimate the optimal elements' values of steady state decoupling compensator unit. The proposed technique is applied on a two thermally Coupled distillation column characterized with four Inputs-four Outputs. This Proposed technique proves remarkable success in minimizing the interaction between the inputs and Outputs except that Output has been proper paired with.