Of late, the discrete Hartley transform (DHT) has become an important real-valued transform. Many fast algorithms for computing the DHT of sequence length N = 2m have been reported. Fast computation of the DHT of length N = q.2m, where q is an odd integer, is proposed. The key feature of the algorithm is its flexibility in the choice of sequence length N, where N need not necessarily be a power of 2, while giving rise to a substantial reduction in computational complexity when compared to other algorithms.