A URV decomposition of a matrix is a factorization of the matrix into the product of a unitary matrix (U), an upper triangular matrix (R), and another unitary matrix (V). In an earlier paper [UMIACS-TR-90-86] it was shown how to update a URV decomposition in such a way that it reveals the effective rank of the matrix. It was also argued that the updating procedure could be implemented in parallel on a linear array of processors; however, no specific algorithms were given. This paper gives a detailed implementation of the updating procedure. (Also cross-referenced as UMIACS-TR-92-44)