This paper proposes a horizontal fragmentation method to preserve privacy in data outsourcing. The basic idea is to identify sensitive tuples, anonymize them based on a privacy model and store them at the external server. The remaining non-sensitive tuples are also stored at the server side. While our method departs from using encryption, it outsources all the data to the server; the two important goals that existing methods are unable to achieve simultaneously. The main application of the method is for scenarios where encrypting or not outsourcing sensitive data may not guarantee the privacy.