The present invention performs a lossless four-point orthogonal transformation with reduced rounding errors using a simple configuration. A data transformation apparatus receives four items of vector data X0, X1, X2, and X3,.times..times. ##EQU00001## and determines D0 to D3 as: D0=X0+aX1+aX2+a.sup.2X3; D1=aX0-X1+a.sup.2X2-aX3; D2=aX0+a.sup.2X1-X2-aX3; and D3=a.sup.2X0-aX1-aX2+X3. Integer data smaller than half a divisor {1+a.sup.2} is added to D1 to determine D1', and a value equal to half the divisor is added to D0, D2, and D3 to determine D0', D2', and D3', respectively. D0', D1', D2', and D3' are divided by the divisor and the results are rounded such that resulting integers are smaller than the results of division, and outputting the resulting integers.