Vertebrate somatic cells sometimes form unilateral furrows during cytokinesis that ingress from only one edge of the cell. In some cases after a cell initiates a normal symmetrical circumferential furrow, one of its edges stops furrowing and regresses while the furrow associated with the opposing edge continues across the cell. In cells containing two independent spindles unilateral furrows are sometimes formed that do not follow a linear path but instead sharply change their direction and wander for >40 microm through the cell. These observations reveal that the 'contractile ring' normally seen during cytokinesis is composed of multiple independent 'furrowing units' that are normally coordinated to form a symmetrical furrow around the cell, and that once formed this so-called contractile band does not function as a 'purse string' as commonly envisioned. Individual furrowing units can work independently of one another, and cytokinesis in vertebrates can be consummated by the formation of a single functional furrowing unit in a localized region of the cell cortex that is then propagated across the cell. How this propagation occurs remains an important question for the future.