  We consider large non-Hermitian real or complex random matrices $X$ with
independent, identically distributed centred entries. We prove that their local
eigenvalue statistics near the spectral edge, the unit circle, coincide with
those of the Ginibre ensemble, i.e. when the matrix elements of $X$ are
Gaussian. This result is the non-Hermitian counterpart of the universality of
the Tracy-Widom distribution at the spectral edges of the Wigner ensemble.
