Privacy and Security of the data are the major concern in Wireless Sensor Networks (WSNs). Many applications which are based on WSN require data exchanges with data privacy intact of the sensed data. Using minimum tree structure can significantly reduce the number of nodes in data transmission. In this paper, we propose a privacy mechanism, STDM, based on Steiner tree and decentralization mechanism in order to provide privacy of the data with minimum number of hops to the sink for WSNs. Simulation results show that STDM performs efficiently compared to some of the existing approaches. It gives high path diversity which guarantees the increase in data privacy. This paper also analyses the performance of STDM with respect to metrics such as path diversity, energy consumption, reliability, communication overhead and computation costs.