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Dynamic subcarrier allocation improves the performance of OFDM systems by exploiting multi-user diversity. Fairness index is a parameter which indicates how fairly the sub-carriers are allocated among the users in a system. A greedy sub-carrier allocation algorithm optimizes the system performance in terms of throughput, but it sacrifices the instantaneous fairness. In this paper, we define a new term called "asymptotic fairness". It is shown that for a small number of users greedy subcarrier allocation algorithm leads to a normalized fairness index close to unity after a few channel realizations; therefore, if the users of the same group can wait for a few OFDM symbols, they all can get almost the same data rate. To generalize the idea for larger number of users, we have proposed grouping of the users into smaller group sizes. The proposed subcarrier allocation algorithm allocates the subcarriers in two steps: group-allocation and user-allocation. Group-allocation is performed to maintain fairness among different groups by using a fairness-oriented subcarrier allocation algorithm such as max-min algorithm. In the user-allocation step, the subcarriers are allocated to the users within the group using the greedy algorithm to maximize the throughput. The proposed algorithm is specifically suitable for non-real-time applications. According to the required average fairness index in the system and the maximum allowable waiting time, it is possible to find the proper group size in the proposed two-step subcarrier allocation.