Fast algorithms of a transform, like fast Fourier transform (FFT) algorithms, are based on different decomposition techniques. It is shown that these decomposition techniques can also be applied to the computation of the discrete Harley transform (DHT) for a real-valued sequence. Recently, an efficient decomposition technique for radix-3 decimation-in-time (DIT) FFT and fast Hartley transform (FHT) algorithms has been demonstrated. In this paper, such a decomposition technique is implemented for radix-3 and -6 decimation-in-frequency (DIF) FHT algorithms and found to improve the operation count.