The authors propose an orthogonal, unitary transformation called the modified Hermite transformation (MHT) and its extension, which is called the modular modified Hermite transformation (MMHT). The MHT algorithm, which is an efficient algorithm, is explained and explored. The MHT is compared to the discrete cosine transform (DCT) for various AR(1) input signal source models using the performance criterion of gain over PCM, denoted by /sup N/G/sub TC/. The MHT algorithm requires only 2N real multiplications or divisions for a transformation of a signal block of N samples. It is also used for the inverse transformation, IMHT, and makes this new transform attractive. It is efficient computationally and comparable to the DCT for AR(1) source models with positive correlation coefficients, it is somewhat better than the DCT for negative correlation coefficients. >