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Millimetre wave (mmWave) communications provide a favourable solution to the ever-increasing data rate demands because of their abundant bandwidth availability. The conventional wisdom about the mmWave communication channel is that it always exhibits line-of-sight (LOS) propagation with directive antennas. However, in mobile communications, mmWave frequencies suffer from frequent LOS blockages and exhibit multipath propagation, which motivates the study and analysis of the polarimetric properties of the mmWave channel. While the exploitation of polarisation is promising, the cross-polarisation associated with it can be detrimental to the overall performance. Therefore, in this Letter, the authors propose a hybrid precoder design, which mitigates the cross-polarisation by the joint design of a radio-frequency beamformer as well as the precoder and combiner used in the baseband. The authors demonstrate through simulations that the proposed design outperforms eigen-beamforming by 10 dB at a given rate, when considering polarisation.