This paper presents a novel chaotic digital communication system that uses an extended Bernoulli map (EBM). We use the discontinuous point of EBM as information carrier. Chaotic signals generated with EBM in which the discontinuous points are modulated by the information to be transmitted are sent to the receiver. The information transmitted to the receiver can be demodulated by a correlation detector. This method can increase the number of transmittable information bits by increasing the number of discontinuous points for modulation. We show the performance of this method using BER.