Reversible watermarking can embed data into the cover image and extract data from stego image, where the original cover image can be recovered perfectly after the extraction of data. Difference expansion (DE) and prediction error expansion (PEE) are two popular reversible watermarking methods. DE has the advantage of small distortion while PEE has the advantage of large embedding capacity and smaller prediction error compared with pixel difference. In this paper, we proposed a novel method that combines the advantages of DE and PEE, where the difference calculated between two pixels is combined with the edge information near this pixel pair. The proposed difference calculation can produce smaller pixel difference compared with the original simple pixel difference calculation. Overlapping embedding is then used to increase the embedding capacity. Our proposed method gives excellent results which is shown by several experiments.