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This paper presents for the first time a method of mathematical synthesis involving chaining of Chebyshev polynomials of the second kind for the application of a dual-band waveguide filter. This method takes advantage of second kind Chebyshev polynomials that have high out-of-band rejection, and overcomes unequal-ripple properties. It is applicable to high filter orders greater than five, and will always possess symmetrical dual-band filter properties. This proposed approach is able to achieve an optimum and constant ripple, the flexibility of return loss, and high adjacent band's rejection. The design method is based on suitably defined transmission zeros at the centred frequency to the chained Chebyshev of the second kind. A sixth-order waveguide filter based on a prescribed return loss of 15 dB centred at a frequency of 28 GHz, with a fractional bandwidth of 1% in each passband, has been implemented and …