In this paper, we investigate the effect of Rayleigh fading on the connectivity of wireless ad hoc networks. We consider static nodes that are equipped with omnidirectional antennas and are randomly distributed in the network according to a uniform distribution. We derive an analytical model for evaluating the impact of Rayleigh fading on the network local connectivity and present an accurate upper bound for 1-connectivity. Furthermore, our numerical results show that the presence of fading can result in an improvement in the overall connectivity, although it reduces the local connectivity of the network.