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Considering the shortcomings of differential chaos shift keying (DCSK) with bad secrecy and low data transfer rate, this study designs and researches a new chaos shift keying digital modulation scheme - frequency-modulated correlation delay shift keying (FM-CDSK). The scheme has both the merits of CDSK and FM-DCSK. This study provides the particular theoretical derivation of the principle of modulation and demodulation. The simulation analysis of data transmission rate and confidentiality verify that this new scheme has more superior performance than DCSK and CDSK, and the transmission rate is twice as much as original shift keying schemes. Meanwhile, this new chaos shift keying scheme perfectly achieves the secrecy transmission of image signal. It can be clearly seen that this scheme is realisable in digital secure communication.