One of the major issues experienced by the IEEE 802.11 standard is the fair sharing of the channel between unicast and multicast flows. This problem is obviously caused by the use of the smallest Contention Window size to transmit the multicast packets compared to an exponentially incremented size for every unicast packet transmission retry. This pattern is due mainly to the reliability degree difference between the unicast and the multicast traffic. Currently, the unicast uses feedbacks to provide reliability, whereas the multicast does not rely on such a mechanism and is therefore considered as unreliable. In this paper we propose a reliable Multicast flow transport proposal called the Reliable PLCP-based Multicast Protocol (RPMP) and we study its impact on the fair channel sharing with unicast flows in high-load conditions. We show that RPMP solves the issues of the legacy multicast.