Eight point Discrete Cosine Transform (DCT) and eight point DCT can be calculated by not more than 8 multiplications by performing a given weighting for each component of orthogonal transformation of DCT and inverse DCT. An orthogonal transformation apparatus can be implemented by one multiplication unit, one addition unit or substraction unit, three butterfly operation units, several resequence units, delay units and selector unit by using one multiplication unit which is capable of one multiplication per one sample on a time-sharing basis.