We analytically and experimentally study the Fraunhofer diffraction of an optical vortex beam possessing noninteger values of the azimuthal index. We show that the Fraunhofer diffraction of this beam presents the birth of a vortex at α=n+ε, where n is an integer number and ε is a small fraction. We discuss this behavior on the basis of the born vortex movement from a position of low intensity to high intensity when α is increased of an integer number in fractional steps of ε.