A new error rate formula for narrowband Differential Quaternary Phase Shift Keyed system in a Rayleigh fading channel is obtained in closed-form. The formula predicts a non-zero error probability for noiseless reception. As predicted, the computed error rates approach some constant or floor values as the signal-to-noise ratio is increased beyond a certain limit. In the presence of various Doppler frequency shifts, an IF filter bandwidth of about one times the symbol rate is found to lead to a minimum error probability prior to the appearence of the error rate floor.