Over multipath channels, complete complementary code division multiple access and convolutional spreading code division multiple access provide inter-channel interference free transmission with an enhanced spectral efficiency. However, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">convolutional spreading</i> (CS) operation of the systems is computationally complex and involves a high peak-to-average power ratio. To address such issues, we propose the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">concatenative complete complementary code</i> (CCCC) division multiple access, named (CCC-CDMA). Since the CCCCs can be generated from the rows of the Walsh-Hadamard or discrete Fourier transform matrices, the CS operation can be implemented using corresponding fast transforms to reduce computational complexity. Simulation results show that the enlargement of the spreading factor strengthens the robustness against clipping noise. The binary CCCC generated by Walsh-Hadamard matrix exhibited excellent robustness against Doppler frequency shifts.