By using an appropriate index mapping and by introducing a unified approach for the development of the radix-2/4 decimation-in-time (DIT) fast Hartley transform (FHT) and complex-valued fast Fourier transform (FFT) algorithms, it is shown that there is a close relationship between the structures of the two algorithms. As a result of this close relationship, it is shown that only a single general butterfly is sufficient to implement the two algorithms. This type of relationship is of significant importance for software and hardware implementations of the algorithms, since this relationship, along with the fact that the DHT (discrete Hartley transform) is an efficient alternative to the DFT (discrete Fourier transform) for real data, makes it possible for a single software or hardware module to be used for the computation of the DHT as well as for the computation of the forward and inverse DFTs for real- or complex-valued data.