The High Efficiency Video Coding (HEVC) standardization process currently underway includes many tools for the coding of intra pictures. HEVC allows for many more intra prediction modes or directions as compared to previous standards. Efficient coding of these modes is therefore important because the modes consume a non-negligible portion of the total bit-stream used for coding intra pictures. In this paper, a predictive coding method is proposed to reduce the number of bits needed for signaling the intra prediction modes, where the spatial angular correlation between the intra prediction mode of the current Prediction Unit (PU) and the neighboring PUs is computed using a few modulo-N arithmetic operations that do not impact encoder or decoder run-times. The proposed method provides similar or greater improvements in compression efficiency as compared to competing tools, while requiring no changes to the existing bit-stream syntax.