The KLD coefficient and the normalized KLD coefficient are proposed to characterize the correlation of multivariable series in order to overcome the intrinsic limitations of the KLD dimension density. Using the uncorrelated or perfectly correlated multivariable series, the upper and the lower bound functions of the KLD dimension density, and furthermore the upper and the lower bounds of the KLD coefficient are analytically deduced. Then, the normalized KLD coefficient is proposed in the paper. The analyses and numerical simulations prove that the changes of correlation of multivariable series can lead to linear variation of the normalized KLD coefficient. The simulations also prove that the normalized KLD coefficient can detect the changes of correlation sensitively, even if these are induced by only two channels of multivariable series. Furthermore, the normalized KLD coefficient can be used to analyze the nonstationary time series. The simulation results of coupled map lattice prove that the normalized KLD coefficient can also be used for the nonlinear system analysis.