In this paper, we present two improved Amati correlations of gamma-ray burst (GRB) data via a powerful statistical tool called copula. After calibrating with the low-redshift GRB data, the improved Amati correlations based on a fiducial ? cold dark matter (?CDM) model with omega(m0) = 0.3 and H (0) = 70 km s(-1) Mpc(-1), and extrapolating the results to the high-redshift GRB data, we obtain the Hubble diagram of GRB data points. Applying these GRB data to constrain the ?CDM model, we find that the improved Amati correlation from copula can give a result well consistent with omega(m0) = 0.3, while the standard Amati and extended Amati correlations do not. This results suggest that when the improved Amati correlation from copula is used in the low-redshift calibration method, the GRB data can be regarded as a viable cosmological explorer. However, the Bayesian information criterion indicates that the standard Amati correlation remains to be favored mildly since it has the least model parameters. Furthermore, once the simultaneous fitting method rather than the low-redshift calibration one is used, there is no apparent evidence that the improved Amati correlation is better than the standard one. Thus, more work needs to be done in the future in order to compare different Amati correlations.