This invention implements a fast lossless transform almost free from a delay with a small calculation amount. The lossless transform can be used to perform lossless coding and lossy coding quickly. A first calculation unit multiplies data D0, D1, D2, and D3 input to the input terminals by respective weighting coefficients {a0, a1, a2, a3} of {½, −½, −½, −½}, and summates the products. A rounding unit in the first calculation unit rounds the sum into an integer and outputs the integer value E. A second calculation unit multiplies the value E by weighting coefficients {b0, b1, b2, b3} of {−1, 1, 1, 1} set for the respective input data, and adds the products to the respective input data. This invention sets, for the relationship between the first and second weighting coefficients, a condition that a0*b0+a1*b1+a2*b2+a3*b3=−2 or 0.