When a Convolutional Neural Network is used for on-the-fly evaluation of continuously updating time-sequences, many redundant convolution operations are performed. We propose the method of Deep Shifting, which remembers previously calculated results of convolution operations in order to minimize the number of calculations. The reduction in complexity is at least a constant and in the best case quadratic. We demonstrate that this method does indeed save significant computation time in a practical implementation, especially when the networks receives a large number of time-frames.