We present the results for the design ofantireflection (AR) coatings on facets of a multilayered structure waveguide device. The method, whose results agree very well with the reusults of the rigorous method in the case of a symmetric three layer structure deveice, is extended for the design of AR coatings on the facets of a multilayered structure waveguide device. the field profile in a multilayered structure waveguide necessary for the use of the extended method is obtained from the transfer matrix method. The virtual four layered structure method (VFLM) is proposed to reduce the time for the design ofAR coatings because the time for the design of AR coatings using the extended method increases as the number of layers increases. The optimum coating parameters and tolerance mapsfor two different six layered waveguide devices in Ref. [9] and [10] are obtained using the extendedmethod and the VFLM,and for the three different cases approximated as three layered waveguide devices to compare the results of each case. The results of the VFLM are similar to those of the extended methodcompared to those of the three layered structure waveguide. The main reason for the above results is that the field profile in the device calculated usingthe VFLM is similar to that calculated using the extended method compared to that for three layered structure wavegjide. We conclude that the extended method or VFLM should be used for the design of AR coatings on facets of a deice required for the facet reflectivity less than 10$^{-3}$ such as a semiconductor otical amplifier.