It is known that every digital covering map p : (E, κ) → (B, λ) has the unique path lifting property. In this paper, we show that its inverse is true when the continuous surjective map p has no conciliator point. Also, we prove that a digital (κ, λ)−continuous surjection p : (E, κ) → (B, λ) is a digital covering map if and only if it is a local isomorphism, when all digital spaces are connected. Moreover, we find out a loop criterion for a digital covering map to be a radius n covering map.