  Let $(G,N)$ be a pair of groups. In this article, first we construct a
relative central extension for the pair $(G,N)$ such that special types of
covering pair of $(G,N)$ are homomorphic image of it. Second, we show that
every perfect pair admits at least one covering pair. Finally, among extending
some properties of perfect groups to perfect pairs, we characterize covering
pairs of a perfect pair $(G,N)$ under some extra assumptions.
