  As a generalization of tilting pair, which was introduced by Miyashita in
\cite{YM}, the notion of silting pair is introduced in this paper. The authors
extends a characterization of tilting modules given by Bazzoni
\cite[Theorem~3.11]{BS} to silting pairs, and proves that there is an
one-to-one correspondence between equivalent classes of silting pairs and
certain subcategories which satisfy some conditions. Furthermore, the authors
also gives a bijection between equivalent class of silting pairs and bounded
above co-t-structure.
