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AQ Men is a nova-like variable which is presumed to have a tilted, precessingaccretion disc. Grazing eclipses in this system have been speculated to beuseful in exploring the geometry of its accretion disc. In this work weanalysed TESS observations of AQ Men, which provide the best light curve ofthis object thus far. We show that the depths of the eclipses are changing withthe orientation of the accretion disc, which means that they can serve as adirect test of the tilted accretion disc models. The precession period of theaccretion disc is increasing during the TESS observations. However, it is stillshorter than the period determined in the previous studies. The amplitude ofthe variability related to the precession of the accretion disc varies, and sodoes the shape of this variability. Moreover, we have detected a positivesuperhump that was previously unseen in AQ Men. Interestingly, the positivesuperhump has a strongly non-sinusoidal shape, which is not expected for anova-like variable.

Exploring the tilted accretion disc of AQ Men with TESS