This paper proposes a universal method for a cascade chaotic system (CCS). CCSs may own better performances, including larger maximum Lyapunov exponents, extended full mapping range of chaos, and more coefficient variations. The chaos-cascade theorems had been proposed in our previous papers, which are more suitable for discrete chaotic systems with the same domain. In this paper, we further improve a universal method to normalize arbitrary discrete chaotic systems for constructing a series of CCSs. Besides, the inheritance and enhancement of robustness from the subsystem are first explored for CCSs. Finally, the designed CCS is implemented on field programmable gate array board. The generated chaotic sequences are obtained by an oscilloscope and tested by NIST software.