A new non-parametric method based on Gaussian Processes (GP) was proposed recently to measure the Hubble constant H0. The freedom in this approach comes in the chosen covariance function, which determines how smooth the process is and how nearby points are correlated. We perform coverage tests with a thousand mock samples within the ΛCDM model in order to determine what covariance function provides the least biased results. The function Matérn(5/2) is the best with sligthly higher errors than other covariance functions, although much more stable when compared to standard parametric analyses.