The fast topology changes in vehicular ad hoc networks (VANETs) may be caused by fading of the wireless link as well as mobility of nodes. Link stability is often measured using mobility parameters (e.g, location, velocity, direction), and disregarding multipath fading of the signal. This may cause network performances degradation. In this paper, we have improved the relay selection scheme by integrating a new routing metric which measures link stability taking into account to the multipath fading statistics basing on contention-based forwarding (CBF) approach. The objective is that to make vehicles able to select the most stable with the minimum fading route from them to the Internet road side units (RSUs). The simulation results show that the proposed protocol enhances throughput and decreases overhead with a comparable end to end delay.