A composite chiral metamaterial (CCMM) is designed and studied both numerically and experimentally. The CCMM is constructed by the combination of a continuous metallic wires structure and a purely chiral metamaterial (CMM) that consists of conjugated Rosettes. For the CMM, only very small, useful bands of negative index can be obtained for circularly polarized waves. These bands are all above the chiral resonance frequencies because of the high value of the effective parameter of relative permittivity epsilon. After the addition of the continuous metallic wires, which provide negative permittivity, the high value of epsilon can be partially compensated. Thus, a negative index band for the left circularly polarized wave that is below the chiral resonance frequency is obtained for the CCMM. At the same time, a negative index band for the right circularly polarized wave that is above the chiral resonance frequency is also obtained. Furthermore, both negative index bands correspond to the transmission peaks and have high values of the figure of merit. Therefore, the CCMM design that is proposed here is more suitable than the CMM for the construction of chiral metamaterials with a negative index. (C) 2012 Optical Society of America