Lapped Orthogonal Transform (LOT) is a new tool for block transform coding with basis functions that overlap adjacent blocks. The LOT can reduce the blocking effect to very low levels. In this paper, an exact derivation of an optimal LOT is presented. The optimal LOT is related to the discrete cosine transform (DCT) in such a way that a fast algorithm for a nearly optimal LOT is derived. Compared to the DCT, the fast LOT requires about 20-30 percent more computations, mostly additions. An image coding example demonstrates the effectiveness of the LOT in reducing blocking effects. Unlike earlier approaches to the reduction of blocking effects, the LOT actually leads to slightly smaller signal reconstruction errors than does the DCT.