We propose and demonstrate a method to obtain polarization-insensitive four-wave mixing in a semiconductor optical amplifier. The method makes use of two pumps with orthogonal polarization placed at the two sides of the signal spectrum. Unlike a previously proposed scheme, a large bandwidth of the signal does not set a lower limit to the degree of polarization insensitivity obtained. Using a commercially available pig-tailed semiconductor optical amplifier, we have obtained less than 0.4 dB of intensity variation of the conjugate field for arbitrary changes of the signal polarization. ©1998 American Institute of Physics.