This paper tries to provide a new perspective for the research of reversible watermarking based on histogram shifting of prediction errors. Instead of obtaining one prediction error for the current pixel, we calculate multiple prediction errors by designing a multi-prediction scheme. An asymmetric error histogram is then constructed by selecting the suitable one from these errors. Compared with traditional symmetric histogram, the asymmetric error histogram reduces the amount of shifted pixels, thus improving the watermarked image quality. Moreover, a complementary embedding strategy is proposed by combining the maximum and minimum error histograms. As the two error histograms shift in the opposite directions during the embedding, some watermarked pixels will be restored to their original values, thus the image quality is further improved. Experimental findings also show that the proposed method re-creates watermarked images of higher quality that carry larger embedding capacity compared to conventional symmetric histogram methods, such as Tsai et al.'s and Luo et al.'s works.