Abstract: This paper deals with the design problem of identical and reduced-order state observers for a completely observable linear multivariable time invariant system x=Ax+Bu,y=Cx.There is developed a new derivation method of state equations for reduced-order observers on the basis of expressions of ordinary algebraic equation solutions;From it,then,a new method is produced by means of a paradigm of complete observability.The method has transformed nonlinear algebraic equations into linear ones,with only a set of linear algebraic equations having (n-r+1) unknown numbers to be solved.Simpler and easier in computations involved and applications,this new method is quite useful,and,what is more favourable,poles of observers may be selected in advance.