Cell shape and movements rely on complex biochemical pathways that regulate actin, microtubules, and substrate adhesions. Some of these pathways act through altering the cortex contractility. Here we examined cellular systems where contractility is enhanced by disassembly of the microtubules. We found that adherent cells, when detached from their substrate, developed a membrane bulge devoid of detectable actin and myosin. A constriction ring at the base of the bulge oscillated from one side of the cell to the other. The movement was accompanied by sequential redistribution of actin and myosin to the membrane. We observed this oscillatory behavior also in cell fragments of various sizes, providing a simplified, nucleus-free system for biophysical studies. Our observations suggest a mechanism based on active gel dynamics and inspired by symmetry breaking of actin gels growing around beads. The proposed mechanism for breakage of the actomyosin cortex may be used for cell polarization.