This paper extends the mathematical synthesis on chaining Chebyshev polynomials of the second kind for the application of a dual-band microstrip filter. The proposed filter allows the flexibility to place multiple inner band transmission zeros for better inner band rejection without affecting the equiripple characteristics of chained Chebyshev polynomials of the second kind. This proposed approach can achieve high adjacent bands' selectivity and optimum ripple levels for both passband and stopband. The design method allows one transmission zero reduction and can be introduced at different locations within inner stopband. An eighth-order microstrip filter centred at a frequency of 3.5 GHz, with a fractional bandwidth of 12 in each passband, has been simulated and fabricated to verify the proposed method. A good agreement is found between the simulated and measured filter responses. The proposed filtering function can also be implemented in various filter fabrication technologies for millimetre-wave applications. © 2020 IEEE.