The enhanced high gain harmonic generation （EHGHG） scheme has been proposed and shown to be able to significantly enhance the performance of HGHG FEL. In this paper we investigate the EHGHG scheme with negative dispersion. The bunching factor at the entrance of the radiator is analyzed, which indicates that the scheme with negative dispersion can further weaken the negative effect of the dispersive strength on the energy spread correction factor. The numerical results from GENESIS （3D-code） are presented, and are in good agreement with our analysis. Then we comparatively study the effects of the initial beam energy spread and the relative phase shift on the radiation power. The results show that the EHGHG scheme with negative dispersion has a larger tolerance on the initial beam energy spread and a nearly equal wide good region of the relative phase shift compared with the case of positive dispersion.
