We have carried out Monte Carlo simulation of the fusion of bilayers of single chain amphiphiles which show phase behavior similar to that of biological lipids. The fusion mechanism we observe is very different from the "stalk" hypothesis. Stalks do form on the first stage of fusion, but they do not grow radially to form a single bilayer diaphragm. Instead, stalk formation destabilizes the membranes and results in hole formation in the vicinity of the stalks. When holes in each bilayer nucleate spontaneously next to the same stalk, an incomplete fusion pore is formed. The fusion process is completed by propagation of the initial connection, the stalk, along the edges of the aligned holes.