Magnetic clouds (MCs), as large-scale interplanetary magnetic flux ropes, are usually still connected to the sun at both ends near 1 AU. Many researchers believe that all non-MC interplanetary coronal mass ejections (ICMEs) also have magnetic flux rope structures, which are inconspicuous because the observing spacecraft crosses the flanks of the rope structures. If so, the field lines of non-MC ICMEs should also be usually connected to the Sun on both ends. Then we want to know whether the field lines of most non-MC ICMEs are still connected to the sun at both ends or not. This study examined the counterstreaming suprathermal electron (CSE) signatures of 266 ICMEs observed by the emph{Advanced Composition Explorer} (emph{ACE}) spacecraft from 1998 to 2008 and compared the CSE signatures of MCs and non-MC ICMEs. Results show that only 10 of the 101 MC events ($9.9%$ ) and 75 of the 171 non-MC events ($43.9%$) have no CSEs. Moreover, 21 of the non-MC ICMEs have high CSE percentages (more than $70%$) and show relatively stable magnetic field components with slight rotations, which are in line with the expectations that spacecraft passes through the flank of magnetic flux ropes. So the 21 events may be magnetic flux ropes but the emph{ACE} spacecraft passes through their flanks of magnetic flux ropes. Considering that most other non-MC events have disordered magnetic fields, we suggest that some non-MC ICMEs inherently have disordered magnetic fields, namely have no magnetic flux rope structures.
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