We investigate a temperature-driven recursive division of binary giant unilamellar vesicles (GUVs). During the heating step of the heating-cooling cycle, the spherical mother vesicle deforms to a budded limiting shape using up the excess area produced by the chain melting of the lipids and then splits off into two daughter vesicles. Upon cooling, the daughter vesicle opens a pore and recovers the spherical shape of the mother vesicle. Our GUVs are composed of DLPE (1,2-dilauroyl-sn-glycero-3-phosphoethanolamine) and DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphocholine). During each cycle, vesicle deformation is monitored by a fast confocal microscope and the images are analyzed to obtain the time evolution of reduced volume and reduced monolayer area difference as the key geometric parameters that quantify vesicle shape. By interpreting the deformation pathway using the area-difference elasticity theory, we conclude that vesicle division relies on (1) a tiny asymmetric distribution of DLPE within the bilayer, which controls the observed deformation from the sphere to the budded shape; and (2) redistribution of DLPE during the deformation-division stage, which ensures that the process is recursive. The spontaneous coupling between membrane curvature and PE lipid distribution is responsible for the observed recursive division of GUVs. These results shed light on the mechanisms of vesicle self-reproduction.