The general conditions of exact reconstruction and a recursive design procedure for lapped orthogonal transform (LOT) with arbitrary length of overlapping are presented. It is shown that LOT can be realized with any standard block transform, discrete cosine transform (DCT), for example, and an additional processing. This processing must also satisfy the same conditions for exact reconfigurations and it may be pretransform processing in the time domain or post-transform processing in the transform domain. In a few examples it is shown that the LOT has a higher coding gain and smaller blocking effects then DCT. With the proposed LOT design procedure, two optimizations, the coding gain maximization and the blocking effect minimization, are presented and compared.