Abstract: For design of minimal order A Kx-observer in frequency domain,it seems more feasible to use the matrix transfer function of the control system directly,so the state space realization of the system is avoided.The designproblem for minimal order Kx-observer in frequency domain is analyzed and the solution to the problem reduces to four conditions.As it is impossible to write all these conditions in analytic form,it is difficult to find out a procedure to meet them.These design conditions are simplified to a great extent with the help of the dual minimal basis（DMB）of polynomial vector spaces and Popov Echelon Form concepts.In consequence,a design procedure for minimal order Kx-observer in frequency domain is given and seems simple.Moreover,the probable minimal order of Kx-observer in frequency domain is discussed.