  In this paper we show that a digital $(\kappa,\lambda)-$continuous surjection
$p:(E,\kappa)\rightarrow (B,\lambda)$ is a digital covering map if and only if
it is a local isomorphism. Moreover, we find a loop criterion for a digital
covering map to be an $n$-radius covering. Also, we show that every digitally
continuous map with unique path lifting property is a digital covering map if
it has no conciliator point.
