PCA is an interative algo. Once you build the leading vector, you subtract it from your data and then build the next. Do you know by any chance why you can't

PCA is an interative algo. Once you build the leading vector, you subtract it from your data and then build the next. Do you know by any chance why you can't use this new method recursively for building the whole SVD basis ? (I haven't read the paper carefully yet.. It's a bit at the limit of my understanding )