In this paper, a novel scheme in enhancing the selectivity of the quasi-elliptic microstrip bandpass filters is presented. A rectangle open-loop resonator is implemented as the cross coupling path in the filter topology. This cross coupling relocates the existing attenuation poles of the quasi-elliptic filter so as to provide higher selectivity. Compared to a traditional six-pole quasi-elliptic filter with a fractional bandwidth of 7.8% and center frequency of 1GHz, this scheme offers additional 20dB rejection improvement at the attenuation pole in the upper rejection band whilst 5dB improvement in the lower rejection band.