An Hadamard transform coding circuit changes a rounding method for each Hadamard transform block to prevent a rounding operation from providing an error biased in one direction, as seen in a picture in its entirety, for data compression and rounding. More specifically, after Hadamard transform there exist decimal parts 0.0, 0.25, 0.5 and 0.75, and if a numerical value is simply rounded off a probability would be increased that the numerical value is biased to increase in absolute value. Accordingly for 0.5 a rounding operation to provide an integer switches for each block. Thus a motion image decoding apparatus can be provided to reduce error accumulation and suppress flickering, color variation and other similar noticeable degradations.