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This paper aims at the realization of a discrete-time lossless scattering system, and proposes a plane-rotation algorithm in which the pipelined processing can be applied. In the proposed method, the CORDIC algorithm is divided into unit operations. The operational cells realizing the individual unit operation are connected in cascade to reconstruct the CORDIC algorithm into a pipeline. This configuration by the cascade connection realizes the pipelined processing and has a high modularity since the structure is a linear array of the unit cells. Next, the operational error in the proposed algorithm is classified into the error due to the finite operation and the error due to the finite word-length. A design for the algorithm is presented based on the result of analysis. The feature of the proposed design method is that the necessary operations can be extracted from the specified range of the finite operation error and the rotation angle, while minimizing the finite word-length error of the algorithm. Finally, application examples are shown for the wave digital filter and the sinusoidal pair oscillator. [ABSTRACT FROM AUTHOR]