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In the first part of this article, we proved a local version of the circularlaw up to the finest scale $N^{-1/2+ \e}$ for non-Hermitian random matrices atany point $z \in \C$ with $||z| - 1| > c $ for any $c>0$ independent of thesize of the matrix. Under the main assumption that the first three moments ofthe matrix elements match those of a standard Gaussian random variable afterproper rescaling, we extend this result to include the edge case $|z|-1=\oo(1)$. Without the vanishing third moment assumption, we prove that thecircular law is valid near the spectral edge $ |z|-1=\oo(1)$ up to scale$N^{-1/4+ \e}$.

The local circular law II: the edge case