We introduce new transforms for efficient compression of image blocks with directional preferences. Each transform, which is an orthogonal basis for a specific direction, is constructed from an eigen-decomposition of a discrete directional Laplacian system matrix. The method is a natural extension of the DCT, expressing the Laplacian in Cartesian coordinates rotated to some predetermined angles. Symmetry properties of the transforms over square domains lead to efficient computation and compact storage of the directional transforms. A version of the directional transforms was implemented within the beyond HEVC software and demonstrated significant improvement for intra block coding.