In this paper, we present a new pseudo-random sequence generator, constructed by the generalized discrete Baker transformation. This new generator is called Cascaded Baker Register Machine (CBRM), which uses the sensitivity of chaotic behaviour and allows the application of automata- and shift-register theory. It is shown that a CBRM has good properties of randomness, such as large periods and high linear complexity. It can provide high cryptographic security with fast encryption speed, and can be realized effectively by both hardware and software.