  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 ${\cal N}=1$ 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.
