Ethernet adopts the well-known Binary Exponential Back-off (BEB) scheme for collision resolution. Operation of the BEB algorithm leads to the last-come-first-serve result among competing users (also known as the "capture effect", which allows a few "winning" users to occupy most of the available bandwidth) and BEB is also unstable for every arrival rate greater than 0. Taking the advantage of the central control unit (access point or base station) in wireless network, we propose a novel scheme, Fixed Collision Rate (FCR) back-off algorithm, which amends the drawbacks of BEB. FCR not only achieves a throughput of 1/e at extremely busy channel, but also share the limited bandwidth among competing users in a fairer way. Operation of FCR scheme relies on estimating number of users and maintains the collision rate at a constant level. A variety of estimation methods are provided in this work. Simulation results with perfect knowledge of number of users are obtained to find the performance upper bound of the proposed scheme.