Cells of mutant strains of the bacterium B. subtilis fail to separate upon dividing, and form long fibers. A given fiber is initially straight, but once it grows to around 100 microns, it buckles and writhes. Soon after this initial instability the fiber rapidly braids up into a plectoneme. Modeling a fiber as a twisted elastic filament in a viscous fluid, we exploit the “natural” frame of space curves to formulate the dynamics of the filament’s shape and twist density. The resulting coupled nonlinear equations are used to display a remarkable nonlinear phenomenon: geometric untwisting of open filaments, in which twist strain relaxes through a transient writhing instability without axial rotation. Experimentally observed motions of the fibers of B. subtilis may be examples of this twisting process.