Neither HI nor CO emission can reveal a significant quantity of so-called dark gas in the interstellar medium (ISM). It is considered that CO-dark molecular gas (DMG), the molecular gas with no or weak CO emission, dominates dark gas. We identified 36 DMG clouds with C$^+$ emission (data from Galactic Observations of Terahertz C+ (GOT C+) project) and HINSA features. Based on uncertainty analysis, optical depth of HI $taurm_{HI}$ of 1 is a reasonable value for most clouds. With the assumption of $taurm_{HI}=1$, these clouds were characterized by excitation temperatures in a range of 20 K to 92 K with a median value of 55 K and volume densities in the range of $6.2times10^1$ cm$^{-3}$ to $1.2times 10^3$ cm$^{-3}$ with a median value of $2.3times 10^2$ cm$^{-3}$. The fraction of DMG column density in the cloud ($frm_{DMG}$) decreases with increasing excitation temperature following an empirical relation $frm_{DMG}=-2.1times 10^{-3}T_(ex,tau_{HI}=1)$+1.0. The relation between $frm_{DMG}$ and total hydrogen column density $N_H$ is given by $frm_{DMG}$=$1.0-3.7times 10^{20}/N_H$. The values of $frm_{DMG}$ in the clouds of low extinction group ($Arm_V le 2.7$ mag) are consistent with the results of the time-dependent, chemical evolutionary model at the age of ~ 10 Myr. Our empirical relation cannot be explained by the chemical evolutionary model for clouds in the high extinction group ($Arm_V > 2.7$ mag). Compared to clouds in the low extinction group ($Arm_V le 2.7$ mag), clouds in the high extinction group ($Arm_V > 2.7$ mag) have comparable volume densities but excitation temperatures that are 1.5 times lower. Moreover, CO abundances in clouds of the high extinction group ($Arm_V > 2.7$ mag) are $6.6times 10^2$ times smaller than the canonical value in the Milky Way. #[Full version of abstract is shown in the text.]#
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