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High Efficiency Video Coding (HEVC) is the latest international standard of video coding under development. In HEVC, the new technology of intra prediction, Unified Directional Intra (UDI), has shown significant improvement on coding performance. Comparing to the intra prediction of H.264/AVC, significant performance improvement was observed for all intra configured tests. In the HEVC Test Model (HM), a predefined angular table is used for generating predicted sample values of UDI. However, how the table is obtained was not clearly presented in the literature. This paper gives a detailed derivation and explanation based on a novel uniform probability model. With this novel model, angular table derivation method was investigated and the selection of table entries used in UDI prediction is well explained. Simulation results show that using the improved angular table proposed in this paper, Bjontegaard Delta (BD)-rate improvement is achieved for sequences with large amount of various textures, in both all intra high efficiency and low complexity configurations.