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The radix-2 decimation-in-time fast Hartley transform algorithm for computing the discrete Hartley transform (DHT) was introduced by Bracewell. A radix-2 decimation-in-frequency algorithm by Meckelburg and Lipka followed. Prado came up with an in-place version of Bracewells decimation-in-time fast Hartley transform algorithm. A set of fast algorithms for both decimation-in-time and decimation-in-frequency was further developed by Sorenson et al. A new fast radix-2 decimation-in-frequency algorithm for computing the DHT that requires less number of multiplications than those presented by Bracewell, Meckelburg and Lipka, Prado and Sorenson et al is proposed. It exploits the characteristics of the DHT matrix, exhibits stage structures with butterflies similar for each stage and introduces multiplying structures in the signal flow diagram. The operation count for the proposed algorithm is determined. It is verified by implementing the program in C.