Transcription analyses reported in these studies reveal that convergent genes in S. pombe generate overlapping transcripts in the G1 phase of the cell cycle. We show that this double-strand (ds) RNA induces localized RNAi (Dicer and RITS) dependent transient heterochromatin structures including histone H3 lysine 9 trimethylation marks and Swi6 association. Consequently cohesin is recruited to these chromosomal positions through interaction with Swi6. In G2, localized cohesin is further concentrated into the intergenic regions of the convergent genes tested. This results in a block to further dsRNA formation by promoting gene-proximal transcription termination between the convergent genes. Cohesin release at mitosis leads to a new G1 phase with repeated dsRNA formation, transient heterochromatin, and cohesin recruitment. Our results uncover a hitherto unanticipated role for cohesin and further suggest a widespread role for the selective formation of dsRNA, heterochromatin, and subsequent cohesin recruitment in regulated transcriptional termination.