Displaced subdivision surface representation [13] is a new form of representing a polygonal surface model, where a detailed surface model is defined as a scaler-valued displacement map over a smooth domain surface; it puts forth a number of attractive features for editing, geometry compression, animation, scalability, and adaptive rendering of polygonal models. The construction of the smooth domain surface is a challenging task in the conversion process of a detailed polygonal surface model into this representation. In this paper, we propose a new efficient method for defining the smooth domain surface based on -subdivision scheme. The proposed algorithm not only performs better in terms of the quality of the generated surfaces but is computationally more efficient and occupies less memory as compared to the original algorithm [13] and generates surfaces with more levels of detail due to the specific nature of -subdivision when the prescribed target complexity of the generated mesh must not be exceeded. To corroborate the efficiency and the quality of the new technique, the conversion results for several public domain models have been presented.