The authors propose a simple new method for fabricating stable nanotips using sharpened Au-Mo alloy tips. By annealing at 1000-1200 K in UHV, Au atoms segregate to the alloy surface to form a Au film of one physical monolayer thickness, resulting in formation of nanopyramids on the (111) surface. Although field ion microscopy images of the nanotips show no single-atom termination similar to the previous cases of Au-deposited W nanotips, energy spectra of the emitted electrons strongly suggest the realization of a single-atom termination just after annealing.