In this paper, the 1/4 wavelength backward-wave directional coupler using coupled lines with finite metallization thickness is described. A mode-matching method, simple and fast approach to the quasi-static analysis, has been used to analyse this structure. The numerical results show that it is possible to overcome the disadvantages of weakly coupling, low directivity, and narrow strip distance non-realizable in the case of 1/4 wavelength backward-wave directional coupler with zero thickness conductor. It is also revealed that thicker metallization causes longer coupler length in the case of backward-wave symmetrical parallel coupled line directional coupler. The finite metallization thickness can be a new parameter for tight coupling in the design of backward-wave directional couplers, which enables us to design more accurate properties of monolithic microwave integrated circuits.