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Evidence suggests that a non-zero dawn–dusk interplanetary magnetic field (IMF B y ) can cause a rotation of the cross-tail current sheet/neutral sheet around its axis aligned with the Sun–Earth line in Earth's magnetotail. We use Geotail, THEMIS and Cluster data to statistically investigate how the rotation of the neutral sheet depends on the sign and magnitude of IMF B y . In our dataset, we find that in the tail range of - 30 < XGSM < - 15 R E , the degree of the neutral sheet rotation is clearly smaller, there appears no significant rotation or even, the rotation is clearly to an unexpected direction for negative IMF B y , compared to positive IMF B y . Comparison to a model by Tsyganenko et al. (2015, doi:10.5194/angeo-33-1-2015) suggests that this asymmetry in the neutral sheet rotation between positive and negative IMF B y conditions is too large to be explained only by the currently known factors. The possible cause of the asymmetry remains unclear. [ABSTRACT FROM AUTHOR]