Septins are polymerizing GTPases that function in cortical organization and cell division. In Saccharomyces cerevisiae they localize at the isthmus between the mother and the daughter cells, where they undergo a transition from a non-dynamic hourglass-shaped assembly to two separate rings, at the onset of cytokinesis. Septins form filaments as pure protein and in vivo, but the filament organization within the hourglass and ring structures is controversial. Here, we use polarized fluorescence microscopy of orientationally constrained green fluorescent protein to determine septin filament organization and dynamics in living yeast. We found that the hourglass is made of filaments aligned along the yeast bud neck. During the transition from hourglass to rings the filaments rotate through 90 degrees in the membrane plane and become circumferential. These data resolve a long-standing controversy in the field and provide strong evidence that septins have a mechanical function in cell division.