J. Schmidt and Cairns (2019) have recently shown that they can predict Coronal Mass Ejection (CME) arrival times with an accuracy of 0.9+-1.9 hours for four separate events. They also showed that the accuracy gets better with increased grid resolution. Here, we further improve these results by using the Richardson extrapolation (Richardson and Gaunt, 1927), which is a standard technique in computational fluid dynamics, and predict the CME arrival time with 0.2+-0.26 hours accuracy. The CME arrival time errors of the new model lie in a 95% confidence interval [-0.21,0.61] h. We also show that the probability of getting these accurate arrival time predictions with a model with a standard deviation exceeding 2 hours is less than 0.1%, indicating that the excellent results cannot be due to random chance, and the Richardson extrapolation has indeed improved the original model by J. Schmidt and Cairns (2019). This unprecedented accuracy is about 40 times better than the current state-of-the-art prediction of CME arrival times with an average error of about +-10 hours. The new model uses information available within a few hours after the CME eruption and it can run much faster than real-time on a couple of CPU cores. Based on the result, we recommend the new model to be transitioned to operations as soon as possible to better protect our space-born and ground-based assets from the harmful effects of space weather.