We consider an algorithm for reduction of broadband noise in speech based on signal subspaces. The algorithm is formulated by means of the quotient singular value decomposition (QSVD). With this formulation, a prewhitening operation becomes an integral part of the algorithm. We demonstrate that this is essential in connection with updating issues in real-time recursive applications. We also illustrate by examples that we are able to achieve a satisfactory quality of the reconstructed signal.