Differently from other image/video compression techniques, it is not easy to find a successful watermarking scheme for H.264/AVC. Thus we, as the researchers on digital watermarking, intend to find the reason(s) of the hardness in this paper. Among the various techniques in H.264/AVC we only concern the intra-prediction in this paper, which is the main technique to form an intra picture. We closely examine the properties of intra-prediction in the aspect of digital watermarking. We consider three watermarking schemes: (1) a blind scheme by fixing the watermark positions without using any information from encoding process, (2) a semi-blind scheme which selects watermark positions with a threshold value of the cost function to determine the prediction mode, and (3) a blind scheme selecting only the blocks predicted by 16 × 16 mode as the one to be watermarked. These three schemes are getting more restricted in selecting the watermarking positions. The experiments showed that none of the three schemes were satisfactory. Even the error rates of the extracted watermark data were getting lower. After examining the data, we found the followings. The intra-prediction of H.264/AVC itself is not reversible. That is, the re-engineering of the intra pictures, which is necessary to extract the embedded watermark, does not guarantee the same results as before re-engineering. The intra-prediction modes in many blocks and the coefficient values are changed in re-engineering. In addition, watermarking and attacks further change the prediction modes and coefficient values, which make the watermarking useless. The reason of changing the prediction modes and the coefficient values, we concluded, is heuristics of the technique. That means the intra-prediction includes many heuristic schemes that cannot recover the data exactly. Consequently a new watermarking method rather than the conventional ones is necessary to find.