Differential quadrature phase shift keying (DQPSK) modulation is attractive in high-speed optical communications because of its resistance to fiber nonlinearities and more efficient use of fiber bandwidth compared to conventional intensity modulation schemes. Because of its wavelength conversion ability and phase preservation, semiconductor optical amplifier (SOA) fourwave mixing (FWM) has attracted much attention. We experimentally study wavelength conversion of 40 Gbit/s (20 Gbaud) non-return-to-zero (NRZ)-DQPSK data using FWM in a quantum dash SOAwith 20 dB gain and 5 dBm output saturation power. Q factor improvement and eye diagram reshaping is shown for up to 3 nm pump-probe detuning and is superior to that reported for a higher gain bulk SOA.