A four-winged chaotic attractor was first observed numerically in a new 4-dimensional system. However, it was found to be a numerical artifact upon further analysis. It actually consists of two (upper and lower) coexisting double-wing chaotic attractors with domains of attraction independent of each other. The reason leading to the confusion is that both double-wing attractors are arbitrarily close to each other so as to cause a numerical error as well as a misunderstanding. By adding a simple linear state feedback term to the system, some similaritics of the system are destroyed, then the controlled system is able to generate diagonal double chaotic attractor which can cross the boundary between the upper and lower attractive domains. With the evolution of dynamical modes, the upper and the lower double-wing chaotic attractors as well as diagonal chaotic attractor are merged into a true four-winged chaotic attractor. At last, the frequency spectrum analysis shows that the four-winged chaotic attractor has extremely wide frequency bandwidth compared with that of the Lorenz system and Chua circuit, which is important in practical applications in communication encryption etc.