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We report on observing a long-wavelength band in low-temperature photoluminescence(PL)spectrum of quaternary Al0.22In0.02Ga0.76N/Al0.38In0.01Ga0.61N multiple quantum wells(MQWs), which were grown over sapphire substrates by a pulsed atomic-layer epitaxy technique. By comparing the excitation-power density and temperature dependence of the PLspectra of MQWs and bulk quaternary AlInGaN layers, we show this emission band to arise from the carrier and/or exciton localization at the quantum well interface disorders. PL data for other radiative transitions in MQWs indicate that excitation-dependent spectra position is determined by screening of the built-in electric field.