Generalising ideas of an earlier work \cite{Bo-Han}, we address the problem of constructing Brane Box Models of what we call the Z-D Type from a new point of view, so as to establish the complete correspondence between these brane setups and orbifold singularities of the non-Abelian G generated by Z_k and D_d under certain group-theoretic constraints to which we refer as the BBM conditions. Moreover, we present a new class of N=1 quiver theories of the ordinary dihedral group d_k as well as the ordinary exceptionals E_{6,7,8} which have non-chiral matter content and discuss issues related to brane setups thereof
