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Yamatani and Saito recently published an interesting method for predicting discrete cosine transform (DCT) coefficients of an image block, which uses partial derivatives of the image at the block boundary points. It estimates partial derivatives the same way for all four side boundary points. In this correspondence, we improve their estimation method for the left and top side boundary points by observing that the decoder can use 1-D DCT of the rightmost column of pixels of the block on the left side and bottom row pixels of the block on the top side instead of using just the DC of these two blocks. It led us to revise their prediction equations. Experimental results show that the cumulative reduction in the size of the first five AC coefficients obtained using their equations is 15.1%, and the same using our equations is 24.6%.