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It is generally hard to find the optimal solution for sub-channel and power allocation for a multiuser Orthogonal Frequency Division Multiplexing (OFDM) system that maximizes the overall system capacity given the proportional rate constraint. Most existing solutions either utilize a suboptimal sub-channel allocation and attempt to compute the optimal power allocation or assume uniform power distribution among sub-channels and attempt to optimize using the sub-channel allocation. It is observed that derived solutions do not necessarily satisfy the proportional rate constraint, also referred to as the fairness constraint, supplied in the problem formulation. This paper proposes an iterative algorithm that computes the optimal power allocation for a given sub-channel allocation scheme. Unlike previous solutions, the proposed solution does not make any assumptions regarding the channels or regarding the proportionality constants. Furthermore, the proposed solution satisfies the proportional rate constraint in the strictest sense and therefore can provide absolute or hard rate guarantees as opposed to soft ones as the case for previous algorithms. Presented numerical example, shows that the our algorithm outperforms the original optimal power allocation algorithm and achieves strict satisfaction of the fairness constraint.