This letter examines the problem of allocating the subcarrier power of the relayed signal in orthogonal frequency division multiplexing (OFDM) based dual-hop systems in which the relay terminal is operated in an Amplify-and-Forward (AF) mode and the source node transmits its signal with a uniform power distribution. In AF relaying systems, both the modulation order and the error control scheme are fixed at the relay node, and thus the potential for increasing the data rate via a suitable allocation of the subcarrier power at the relay node does not exist. Therefore, this study proposes an alternative subcarrier power allocation scheme in which the objective is to scale the power assigned to each of the relayed signal sub-carriers in such a way as to minimize the equivalent average noise power at the destination terminal.