  We study the relationship between the partially synchronous state and the
coupling structure in general dynamical systems. Our results show that, on the
contrary to the widely accepted concept, topological symmetry in a coupling
structure is the sufficient condition but not the necessary condition.
Furthermore, we find the necessary and sufficient condition for the existence
of the partial synchronization and develop a method to obtain all of the
existing partially synchronous solutions for all nonspecific dynamics from a
very large number of possible candidates.
