Nearly all block-based transform schemes for image and video coding developed so far choose the 2-D discrete cosine transform (DCT) of a square block shape. With almost no exception, this conventional DCT is implemented separately through two 1-D transforms, one along the vertical direction and another along the horizontal direction. In this paper, we develop a new block-based DCT framework in which the first transform may follow a direction other than the vertical or horizontal one, while the second transform is arranged to be a horizontal one. Compared to the conventional DCT, the resulting directional DCT framework is able to provide a better coding performance for image blocks that contain directional edges - a popular scenario in many image signals. By choosing the best from all directional DCT's (including the conventional DCT as a special case) for each image block, we will demonstrate that the rate-distortion coding performance can be improved remarkably.