In many fields of signal and image processing, control, and telecommunication there is much interest today in the numerical techniques offered by linear algebra. The singular value decomposition (SVD) is one of the techniques which have proven useful in many engineering applications, but unfortunately its computation is a costly procedure. The QR Factorization (QRF) requires much less computational effort, but rank and null-space estimates are not necessarily reliable. T. F. Chan and L. V. Foster developed an algorithm which guarantees the QRF to reveal the rank of a matrix. The main purpose of this paper is to present a version of this Rank Revealing QR (RRQR) algorithm which is suited for implementation on a VLSI systolic array. The implementation of the RRQRF that we propose in this paper requires n(n+1)/2 processors and O(n) external buffers, for a problem of order n. The execution time for the algorithm is O(nr), where r is A's numerical rank.