Block-transform coding is one of the most popular approaches for image compression. For example, DCT is widely used in the internaltional standards standards such as MPEG-1, MPEG-2, JPEG, and H.261. In the block-based transform coding, blocking artifacts may appear along block boundaries, and they can cause severe image degradation eqpecially when the transform coefficients are coarsely quantized. In this paper, we propose a new method for blocking artifacts reduction in transform-coded images. For blocking artifacts reduction, we add a correction term, on a block basis, composed of a linear combination of 28 basis images that are orthonormal on block boundaries. We select 28 DCT kernel functions of which boundary values are linearly independent, and Gram-Schmidt process is applied to the boundary values in order to obtain 28 boundary-orthonormal basis images. A threshold of bolock discontinuity is introduced for improvement of visual quality by reducing image blurring. We also investigate the number of basis images needed for efficient blocking artifacts reduction when the compression ratio changes.