In　this　paper,　the　notion　of　crosstalk-free　rearrangeability　(CF-rearrangeability)　of　multistage　interconnection　networks　(MINs)　is　formally　defined.　Using　the　concept　of　line　digraphs　from　graph　theory,　we　show　that　the　problem　of　crosstalk-free　routing　on　any　bit　permutation　network　(BPN)　is　always　equivalent　to　the　classical　permutation　routing　problem　on　a　BPN　of　smaller　size　and　with　fewer　stages.　We　also　show　the　CF-rearrangeability　and　minimality　(in　stage　number)　of　three　families　of　BPNs,　including　the　dilated　Benes　network.　Some　necessary　conditions　for　a　BPN　to　be　CF-rearrangeable　are　given,　and　a　brief　discussion　of　CF-rearrangeable　networks　with　dilation　in　time　or　space　is　included.