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Polarization-independent all-optical wavelength conversion is demonstrated by using cross-phase modulation in a twisted fiber and subsequent optical filtering. By twisting a 1-km-long fiber at a rate of 15 turns/m and aligning the probe light to circular polarization, we reduce the polarization sensitivity successfully from 3.5 to 0.3 dB. Error-free operation with only 1-dB penalty is realized at 40 Gb/s with the input signal polarization scrambled. The demonstrated scheme also offers a novel function of restoring the degree-of-polarization of the signal light.