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A novel dual-mode resonator with square-patch or corner-cut elements located at four corners of a conventional microstrip loop resonator is proposed. One of these patches or corner cuts is called the perturbation element, while the others are called reference elements. In the proposed design method, the transmission zeros are created or eliminated without sacrificing the passband response by changing the perturbation's size depending on the size of the reference elements. A simple transmission-line model is used to calculate the frequencies of the two transmission zeros. It is shown that the nature of the coupling between the degenerate modes determines the type of filter characteristic, whether it is Chebyshev or elliptic. Finally, two dual-mode microstrip bandpass filters are designed and realized using degenerate modes of the novel dual-mode resonator. The filters are evaluated by experiment and simulation with very good agreement.