A motion picture coding apparatus configured to divide an image into plural slices and divide the plural slices into blocks and code the plural blocks of the image, the motion picture coding apparatus comprising: a mode determination part configured to determine for each of the plural blocks a coding mode wherein the respective coding mode is one of a plurality of coding modes which include a first coding mode of separating a to-be-processed block into a block of DC components and a block of AC components for carrying out the coding; a position determination part configured to determine, based on rate information, for each of the plural blocks, a position of coefficients to be replaced by "0" among coefficients of the plural blocks after orthogonal transformation according to the determined coding mode; a boundary determination part configured to determine whether the to-be-processed block of the plural blocks is a first block below a slice boundary for which referring to pixel values of an upward adjacent block is not allowed; a position changing part configured to change, in case a coding mode of the to-be-processed block is determined as the first coding mode and the to-be-processed block is the first block determined by the boundary determination part, for coefficients of the block of DC components of the to-be-processed block, the position of coefficients to be replaced by "0" determined by the position determination part so that the number of coefficients to be replaced by "0" is reduced, and to output the changed position to a coefficient cutting part, otherwise to output, to the coefficient cutting part, the position of coefficients to be replaced by "0" determined by the position determination part; and the coefficient cutting part configured to replace the coefficients of the to-be-processed block by "0" based on the position received by the position changing part. a mode determination part configured to determine for each of the plural blocks a coding mode wherein the respective coding mode is one of a plurality of coding modes which include a first coding mode of separating a to-be-processed block into a block of DC components and a block of AC components for carrying out the coding; a position determination part configured to determine, based on rate information, for each of the plural blocks, a position of coefficients to be replaced by "0" among coefficients of the plural blocks after orthogonal transformation according to the determined coding mode; a boundary determination part configured to determine whether the to-be-processed block of the plural blocks is a first block below a slice boundary for which referring to pixel values of an upward adjacent block is not allowed; a position changing part configured to change, in case a coding mode of the to-be-processed block is determined as the first coding mode and the to-be-processed block is the first block determined by the boundary determination part, for coefficients of the block of DC components of the to-be-processed block, the position of coefficients to be replaced by "0" determined by the position determination part so that the number of coefficients to be replaced by "0" is reduced, and to output the changed position to a coefficient cutting part, otherwise to output, to the coefficient cutting part, the position of coefficients to be replaced by "0" determined by the position determination part; and the coefficient cutting part configured to replace the coefficients of the to-be-processed block by "0" based on the position received by the position changing part.