Cluster magnetotail data together with ACE solar wind data from 2001 to 2009 are used to investigate the dependence of the azimuthal flow direction of earthward magnetotail fast flows on the interplanetary magnetic field (IMF). We find an indication that fast flows have favored azimuthal directions that have dependence on the IMF. Our results suggest that for positive IMF B_y, the favored azimuthal direction of the fast flows is dawnward in the northern plasma sheet and duskward in the southern plasma sheet. For negative IMF B_y, an opposite situation takes place, the favored azimuthal flow directions are then duskward and dawnward in the northern and southern plasma sheet, respectively. As a possible explanation for the results, it is suggested that the untwisting reconnected magnetic field lines may direct the fast flows in the magnetotail, the field line twist itself being dependent on the IMF.