Use of block-diagonalization of the Jacobian matrix in bifurcation analysis of symmetric systems was demonstrated in Chap. 12. By taking advantage of the underlying geometrical structure of dihedral group symmetry, we give a systematic procedure to determine the transformation matrix for block-diagonalization and an efficient method to compute the block-diagonal form. Group representation theory in Chap. 7, theory of block-diagonalization in Chap. 8, and the application of these theories to the dihedral group in Chap. 9 form a foundation of this chapter.