Taking advantage of Gaussian process (GP), we obtain an improved estimate the Hubble constant, $H_0=70.41\pm1.58$ km s$^{-1}$ Mpc$^{-1}$, using parameter [$H(z)$] from cosmic chronometers (CCH) and expansion rate function [$E(z)$], extracted type Ia supernovae, data. We also use CCH data, including ones with full covariance matrix, $E(z)$ data to a determination $H_0=72.34_{-1.92}^{+1.90}$ whic...