Abstract: A picture encoding system which performs a prediction of picture element values within a block having a plurality of picture elements into which an original picture is divided, a discrete sine transform with respect to prediction error signals for obtaining a transform coefficient, a quantization of the transform coefficient for encoding quantized indexes, an inverse quantization of the quantized indexes for reproduction of the transform coefficient, an inverse discrete sine transform of the reproduced coefficient to reproduce the prediction error signal, and an addition thereto of the predicted picture element value for reproducing the picture element values within the block to employ them in predicting a next stage block to be encoded, whereby the block can be minimized in size while simplifying required transform operation.