The queue management scheme in a router is critical for computer networks because it not only controls the fairness of bandwidth sharing among competing flows, but also contributes to enhancing the efficiency of congestion control algorithms. In this paper, a new queue management scheme, Early Discriminative Dropping (EDD), is proposed to make routers fairer. EDD employs a single queue. In addition, this scheme consists of three main components. Firstly, a threshold estimator evaluates control thresholds based on queue status and the number of accepted packets. Secondly, a quota estimator allocates quotas, which prevent arriving packets of non-aggressive flows from being discarded during congested traffic. Finally, a simple packet-dropping algorithm determines acceptance or discarding of the arriving packet according to current control threshold and available quotas. Using computer simulations, we show that the EDD scheme demonstrates robust and excellent fairness compared with Rotating Preference Queues, Core-stateless Fair Queueing, Dynamic Detection and Expulsion, CHOose and Keep for responsive flows, CHOose and Kill for unresponsive flows and First In First Out under various network topologies and traffic conditions. EDD has a complexity of O(1). Hence, it is feasible for deployment in computer networks where high-performance and high-speed routers exist.