In this paper the method of least squares is employed to design an axially symmetric contradirectional multisection coupled - line coupler together with the impedance matching of real generator and load impedances. An error function is constructed for the required coupling (C) based on the squared magnitude of the ratio of the coupler voltage to that at the incident port. Another algorithm based on the reflected and transmitted wave amplitudes is developed by the method of least squares for the design of a coupled - line coupler with impedance matching of different input and output complex impedances and arbitrary coupling and length. The error functions are minimized to determine the coupler geometry, namely the normalized strip conductor widths (u=w/h) and separation (g=s/h) and the coupler length, where h is the substrate thickness. A procedure is presented to provide the initial values of u and g. The computer implementation of the proposed method shows that a proper coupler design is possible for any given coupler length. This is particularly interesting where space limitations impose contraints on the coupler length. The results are favorably compared with available computer simulation softwares.