Over the past decade, several biclustering approaches have been published in the field of gene expression data analysis. Despite of huge diversity regarding the mathematical concepts of the different biclustering methods, many of them can be related to the singular value decomposition (SVD). Recently, a sparse SVD approach (SSVD) has been proposed to reveal biclusters in gene expression data. In this article, we propose to incorporate stability selection to improve this method. Stability selection is a subsampling-based variable selection that allows to control Type I error rates. The here proposed S4VD algorithm incorporates this subsampling approach to find stable biclusters, and to estimate the selection probabilities of genes and samples to belong to the biclusters.