Most of data in various forms contain sensitive information about individuals and so publishing such data might violate privacy. Privacy preserving data publishing (PPDP) is an essential for publishing useful data while preserving privacy. Anonymization, which is a utility based privacy preserving approach, helps hiding the identities of data subjects and also provides data utility. Since data utility is effective on the accuracy of analysis model, new anonymization algorithms to improve data utility are always required. Mondrian is one of the near-optimal anonymization models that presents high data utility and is frequently used for PPDP. However, the upper bound problem of Mondrian causes a decrease in potential data utility. This article focuses on this problem and proposes a new utility-aware anonymization model (u-Mondrian). Experimental results have shown that u-Mondrian presents an acceptable solution to the upper bound problem, increases total data utility and presents higher data utility than Mondrian for different partitioning strategies and datasets.