We present a new algorithm to compute the QR factorization of a matrix A_m×n intended for use when m ≫ n. The algorithm uses a reduction strategy to perform the factorization which in turn allows a good degree of parallelism. It is then integrated into a parallel implementation of the QR factorization with column pivoting algorithm due to Golub and Van Loan, which allows the determination of the rank of A. The algorithms were coded in Fuportran 90 using the MPI library. Results are presented for several different problem sizes on an IBM 9076 SP/2 parallel computer.