A new discrete orthogonal transform for input data sequences with composite number size is proposed in this paper. The introduced transform is named the discrete Tchebichef-like transform (DTLT). This transform generalizes the discrete Tchebichef transform (DTT). The matrix of DTLT is formed as a Kronecker product of small-sized matrices of DTT. A fast algorithm for computing the proposed transform was developed. Examples of constructing DTLT algorithms for two different lengths of source data sequences that are products of positive integers are given. The corresponding data flow graphs are shown. The introduced transformation was applied to speech signal denoising. A comparison of DTLT with the discrete cosine transform (DCT) showed that DTLT is more robust to white Gaussian noise. In addition, DTLT has lower computational complexity than DCT.