Edelman, AlanStewart, G. W.In updating algorthms where orthogonal transformations are accumulated, it is important to preserve the orthogonality of the product in the presence of rounding error. Moonen, Van Dooren, and Vandewalle have pointed out that simply normalizing the columns of the product tends to preserve orthogonality\,---\,though not, as DeGroat points out, to working precision. In this note we give an analysis of the phenomenon. (Also cross-referenced as UMIACS-TR-92-43)en-USTechnical Report