The differential equation with delayed feedback of the optical bistable system is discretized into a two-dimensional mapping. It is shown that the four-fold oscil-lation mode presents instead of single-mode oscillation upon the loss of stability of the system and that the four modes enter chaos with period-doubling cascade independently with the change of parameter A. In addition, a coexisting attractor is found in the window of period-three. The basin of the coexisting attractor is a fractal structure similar to the two-dimensional Mandeblort set.