This paper further analyzes some basic properties of a new complex four-dimensional continuous autonomous chaotic system, in which each equation contains a cubic cross-product term. The new system has 9 equilibria which display graceful symmetry with respect to the origin and coordinate planes, and they are similar with respect to their linearized characteristics and invariant manifolds. Two coexisting symmetric double-wing chaotic attractors are described. Finally, an analog circuit is designed to implement the new system, which shows a good agreement between numerical simulation and experimental results, and explains their significant distinction in applications due to difference in frequencies.