New findings have been identified recently for chaos application in communication systems, including the simplest matched filter to maximize the signal-to-noise ratio (SNR) and the ability to resist multi-path propagation. However, chaos has a broad band frequency spectrum, which impedes its application in the conventional wireless communication systems due to the antenna and transducer bandwidth. To deal with such problem, the chaos generated by a second order hybrid system (SOHS) with a fixed basis function is used for Differential Chaos Shift Keying (DCSK) communication. A sinusoidal and its orthogonal signal are used to separate the reference signal and the information bearing signal, which are transmitted in the wireless channel. In such a way, the obstacle to broadband signal transmission in a wireless channel is overcome. A matched filter, using the convolution of the received signal and the time reverse of the basis function, maximizes the SNR at the receiver. Moreover, the proposed SOHS-DCSK provides an additional bitstream due to the chaotic signal generated by the SOHS, being capable to encode information as well. The two information sub-streams can be transmitted simultaneously in the proposed method, which possesses different bit transmission rates and reliability. In this way, the High Priority (HP) information bits are transmitted at a low transmission rate, while the Low Priority (LP) information bits are transmitted at a higher transmission rate. Hence, the proposed SOHS-DCSK method not only provides a higher data transmission rate as compared to the conventional DCSK but also makes the transmitted signal to be compatible with the conventional transducer and antenna. Due to the matched filter used, the proposed method achieves a lower bit error rate of the HP information as compared to the other existing enhanced DCSK variants for both additive white Gaussian noise channel and wireless communication channel. The numerical simulations and experiments based on the wireless open-access research platform show the validity and superiority of the proposed method. INDEX TERMS Chaotic shape forming filter, matched filter, DCSK, wireless communication.