This paper continues the researches on a recently proposed reversible watermarking approach based on an integer transform defined for pairs of pixels. The transform is invertible and, besides, for some pairs of pixels, the original values are recovered even if the LSBs of the transformed pixels are overwritten. Two watermarking schemes, a simple one and a modified version, have been developed to embed watermarks into image LSB plane without any other data compression. At detection, original image is exactly recovered by using a simple map which keeps track of the transformed pairs and the LSBs of the unchanged pairs of pixels. The main contribution of this paper is the generalization of the transform for groups of n pixels, where n ≥ 2. Transforming groups larger than 2 pixels, the size of the map decreases and thus, the hiding capacity of the scheme can increase. In this general context, it appears that the behavior of the transform depends on the parity of n i.e., n even is more appropriate for reversible watermarking. It is also shown that, for n ≥ 4 the simple scheme and the modified one give very similar data hiding capacity, i.e., the same performance is obtained at a lower computational cost.