We present a new parallel sorting algorithm that uses a fixed-size sorter iteratively to sort inputs of arbitrary size. A parallel sorting architecture based on this algorithm is proposed. This architecture consists of three components, linear arrays that support constant-time operations, a multilevel sorting network, and a termination detection tree, all operating concurrently in systolic processing fashion. The structure of this sorting architecture is simple and regular, highly suitable for VLSI realization. Theoretical analysis and experimental data indicate that the performance of this architecture is likely to be excellent in practice.