1Department of Mathematics, Hakim Sabzevari University, P. O. Box 96179-76487, Sabzevar, Iran
2Department of Mathematics, Department of Mathematics, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad, Iran.
3Department of Mathematics, Center of Excellence in Analysis on Algebraic Struc- tures, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad, Iran.
Let (G;N) be a pair of groups. In this article, first we con- struct 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.