We propose a new subchannel assignment algorithm for the problem of energy-efficient allocation of subchannels and powers to users for a single-cell OFDMA downlink transmission. It is well known that the joint allocation of subchannels and power for maximizing the energy efficiency of transmission is time-consuming due to the non-convexity of the objective function. Recently, the problem of energy-efficient resource allocation OFDMA-based downlink transmission has been formulated as a two-step allocation process: the first step for subchannel assignment and the second step for power allocation. This paper proposes a low-complexity suboptimal algorithm for assigning subchannels. Applying the Charnes-Cooper Transformation technique and by using the outcome of the proposed subchannel assignment algorithm, we are able to allocate optimum power for each user by solving a single-variable non-linear equation under proportional rate constraints. Numerical results demonstrate that the proposed subchannel assignment algorithm improves both energy and spectral efficiencies compared to the existing ones in the literature.