The difference from 4 to 6 $σ$ in the Hubble constant (H0 ) between the values observed with the local (Cepheids and Supernovae Ia, SNe Ia) and the high-z probes (Cosmic Microwave Background obtained by the Planck data) still challenges the astrophysics and cosmology community. Previous analysis has shown that there is an evolution in the Hubble constant that scales as f (z) = H0/(1 + z)$η$, where H0 is H0 (z = 0) and $η$ is the evolutionary parameter. Here, we investigate if this evolution still holds by using the SNe Ia gathered in the Pantheon sample and the Baryon Acoustic Oscillations. We assume H0 = 70 km s−1 Mpc−1 as the local value and divide the Pantheon into three bins ordered in increasing values of redshift. Similar to our previous analysis but varying two cosmological parameters contemporaneously (H0, $Ømega$0m in the $Łambda$CDM model and H0, wa in the w0waCDM model), for each bin we implement a Markov-Chain Monte Carlo analysis (MCMC) obtaining the value of H0 assuming Gaussian priors to restrict the parameters spaces to values we expect from our prior knowledge of the current cosmological models and to avoid phantom Dark Energy models with w textless −1. Subsequently, the values of H0 are fitted with the model f (z). Our results show that a decreasing trend with $η$ ∼ 10−2 is still visible in this sample. The $η$ coefficient reaches zero in 2.0 $σ$ for the $Łambda$CDM model up to 5.8 $σ$ for w0waCDM model. This trend, if not due to statistical fluctuations, could be explained through a hidden astrophysical bias, such as the effect of stretch evolution, or it requires new theoretical models, a possible proposition is the modified gravity theories, f (R). This analysis is meant to further cast light on the evolution of H0 and it does not specifically focus on constraining the other parameters. This work is also a preparatory to understand how the combined probes still show an evolution of the H0 by redshift and what is the current status of simulations on GRB cosmology to obtain the uncertainties on the $Ømega$0m comparable with the ones achieved through SNe Ia.