Abstract: In order to get miniaturized high-performance filters, based on analyzing the impact of transmission zeros on the selectivity of a filter a new design method was proposed for maximizing the band-edge selectivity of general Chebyshev filters with a minimum filter order. Based on maximizing the band-edge selectivity, the transmission zero of a general Chebyshev filter was obtained accurately from the relationship between the transmission zeros and the frequencies of magnitude characteristic extreme values. A rectangular three-cavity filter, as an example, was optimized. On the basis of meeting the design specifications, the maximum selectivity of the filter was achieved. The measured transmission zero is 850.200 MHz, and the frequency of magnitude characteristic extreme value is 824 MHz. Compared with the traditional filter, the general Chebyshev filter has a narrow transition band and improves the selectivity. The example show that the design method can effectively improve the performance of a filter.