Proper control of epithelial morphogenesis is vital to development and is often disrupted in disease. After germ band extension, the cells of the Drosophila ventral embryonic epidermis are packed in a two-dimensional polygonal array. Although epithelial cell rearrangements are being studied productively in several tissues, the ventral epidermis is of particular interest as the final cell arrangement is, uniquely, far from equilibrium. We show that over the course of several hours, a subset of cells within each parasegment adopts a rectilinear configuration and aligns into parallel columns. Live imaging shows that this is accomplished by the shrinkage of select cell interfaces, as three-cell junctions are converted to four-cell junctions. Additionally, we show that non-muscle Myosin II and the polarity proteins Discs large (Dlg) and Bazooka are enriched along cell interfaces in a complex but reproducible pattern that suggests their involvement in junctional conversion and cell alignment. Indeed, depletion of Myosin II or dlg disrupts these processes. These results show that tight spatial regulation of actomyosin contractility is required to produce this high-energy arrangement of cells.