We propose a systolic architecture for computing a singular value decomposition of an m x n matrix, where $m \geq n$. Our algorithm is stable and requires only $O(mn)$ time on a linear array of $O(n)$ processors. Extensions to algorithms for two-dimensional arrays are also discussed. Key Words and Phrases: Systolic arrays, singular value decomposition, Hestenes method, threshold Jacobi method, real-time computation.