Diminished chords are always ignored by musicians when they learn music theroy. Musicians and music theorists always study the properties and relations of Major and Minor chords or Consonant chords. In Neo-Riemannian theory of TI and PLR groups, he suggest a way of applying Dihedral group,$D_{12}$ to study the relation of Consonant chords. In this paper we will introduce some concepts of group theory to understand the algebraic relationship between the Diminished chords