This study derived the inter-conversion matrices, which can be used in heterogeneous image transcoding between the compressed images using different transforms, such as the $8{ imes}8$ block discrete cosine transform (BDCT) and the one-level discrete wavelet transform (DWT). Basically, to obtain the one-level DWT coefficients from $8{ imes}8$ BDCT, inverse BDCT should be performed followed by forward DWT, and vice versa. On the other hand, if the proposed interconversion approach is used, only one inter-conversion matrix multiplication makes the corresponding transcoding possible. Both theoretical and experimental analyses showed that the amount of computation of the proposed approach decreases over 20% when the inter-conversion matrices are used under specific conditions.