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High-order quasi-reflectionless bandpass filters with improved passband flatness and good impedance matching both in-band and out-of-band are proposed in this work. The proposed design consists of conventional coupled-lines bandpass sections loaded with the presented absorptive stubs at the input and output. Analysis shows that the absorptive stub is equivalent to a 2-pole bandstop filter. Compared to the prior art, the higher-order nature of the presented absorptive stub enables a flatter passband and better out-of-band rejection. The overall filter stopband attenuation can be readily improved by increasing the number of coupled-lines sections without altering the passband responses. Furthermore, cross-coupling between the two absorptive stubs can be used to improve the out-of-band rejection by introducing two transmission zeros without affecting the absorption characteristics. The proposed design concepts are experimentally validated by the design and fabrication of a set of 2.4-GHz 1-, 2-, and 3-pole microstrip quasi-reflectionless bandpass filters. Measured frequency responses of these filters closely match those of the simulation.