This paper presents a unified coupling-matrix synthesis method for microstrip quadruplet bandpass filter on λ/4 resonators. The mainline is implemented with cascading four λ/4 resonators via alternative J and K inverters, while the weak cross coupling path is created with a J inverter between the 1st and 4th λ/4 resonators. The resultant bandpass filter features a generalized Chebyshev in-band frequency response with a pair of determined finite transmission zeros. All the values of pertained J and K inverters are synthesized from the coupling matrix and judiciously extracted based on the fullwave simulation. Finally, a microstrip quadruplet bandpass filter centering at 2.4 GHz with a fractional bandwidth of 10.0% is designed via the proposed synthesis approach. The predicted filtering frequency responses are verified by both fullwave simulated and measured results.