Planar cell polarity (PCP), the coordinated and consistent orientation of cells in the plane of epithelial sheets, is a fundamental and conserved property of animals and plants. Up to now, the smallest unit expressing PCP has been considered to be an entire single cell. We report that, in the larval epidermis of Drosophila, different subdomains of one cell can have opposite polarities. In larvae, PCP is driven by the Dachsous/Fat system; we show that the polarity of a subdomain within one cell is its response to levels of Dachsous/Fat in the membranes of contacting cells. During larval development, cells rearrange (Saavedra et al., 2014) and when two subdomains of a single cell have different types of neighbouring cells, then these subdomains can become polarised in opposite directions. We conclude that polarisation depends on a local comparison of the amounts of Dachsous and Fat within opposing regions of a cell's membrane.