This continues the study on generalized mutiple decomposition allowing 2-way interconnection [1]. Let NeZ+.An automaton M e D, T,F> is an N-automaton iff the set of states D ≤ πSi and each Si e πi (D) where πi is the projection map onto the ith component. Since the states in an N-automation are N-tuples, we may interpret M as consisting of N component automata Ml,..MN, where Mi e i, πSj,fi> for each i.If (sl,..sN,t)e D(F),then fi (si,(πsi,t))e πi(F((sl,..SN),t). We call an N-automation M e D,T,F> a generalized N-decomposition (GND) of M e if M realizes M. Any GND of M induces a set of N *-covers on S. A sufficient condition for a set of *-covers to give rise to a GND is established. The Properties of a GND can be represented by a matrix of relations. The diagonal entries are induced by the components and the off-diagonal entries represent the interconnections.The conditions which give rise to zero connection lines are then determined.