With increasing opportunities for cheaper outsourcing of data, more and more organizations are seriously considering this option to reduce storage and processing costs. However, it has also given rise to the possibilities of security and privacy violations of data in outsourced environments. In this paper, we look at the privacy aspect, often referred to as data confidentiality. Our solution employs partitioning of the data into fragments (horizontal and vertical) so that only that group of fragments which do not violate the privacy are outsourced and the remaining are retained by the owner. The primary objective of the partitioning algorithm is to maximize the size of the outsourced fragment. Since obtaining optimal fragments that satisfy the privacy constraints is NP-hard, we suggest the use of clustering algorithms to provide near-optimal solutions. We provide proof of correctness for the proposed algorithm. We illustrate the proposed scheme using an example and show its efficacy.