The IEEE 802.11 protocol has become the de facto standard in wireless LANs. However, it reveals the unfairness problem between unicast flows and multicast flows since multicast packets are not subject to binary exponential backoff. To prevent a multicast flow from overwhelming the wireless link bandwidth is a crucial issue. This paper seeks to achieve fairness between unicast and multicast flows by introducing Unicast-Friendly Multicast (UFM). The central idea behind the UFM algorithm is to dynamically change the contention window size for multicast packets to limit the bandwidth share of a multicast flow equal to that of a unicast flow. The proposed UFM algorithm adjusts the multicast contention window size depending on the number of competing stations. We present two versions of UFM: the first one calculates the multicast window size by inferring the average contention window size of unicast flows, while the second one maintains the mapping table between the number of competing stations and the corresponding multicast window size given by related analysis. Simulation reveals that both versions of UFM achieve the fairness by providing almost the fair share of bandwidth to each flow regardless of unicast or multicast under the saturated network conditions.