In the paper, we have exploited the use of Gauss-Jordan factorisation to simplify the design of a multivariable system. It shows that the effects of closing a multivariable feedback system in sequential order can also be obtained by performing successive Gauss-Jordan eliminations on its return difference matrix. This simple elimination procedure enables us to transform a multivariable design into a series of multiinput single-output designs and to develop new sequential design procedures with which the well known Nyquist and root loci techniques can be applied. The design of the precompensator K(s) can then be decomposed into n stages such that each column of K(s) can be designed sequentially.