In recent literature, the discrete Stockwell Transform (DST) for infinite length signals has been introduced along with its fast implementation. This method allows for low computational cost and enables processing of an infinite-length or large-size signal segment-by-segment while overcoming the boundary effects produced by conventional DST. The algorithm also preserves the absolute-reference phase, making it suitable for real-time signal processing. In this paper, we propose a new formulation of the discrete Orthogonal Stockwell Transform for infinite length signals. Based on the definition, we implement its fast algorithm using FFT. Our proposed scheme can process an infinite signal segment-by-segment, eliminating boundary effects and preserving the absolute-reference phase. Compared to the DST for infinite length signals, the DOST version significantly reduces computational complexity, making it more practical for real-time signal processing.