Following the success of hashing methods for multidimensional indexing, more and more works are interested in embedding visual feature space in compact hash codes. Such approaches are not an alternative to using index structures but a complementary way to reduce both the memory usage and the distance computation cost. Several data dependent hash functions have notably been proposed to closely fit data distribution and provide better selectivity than usual random projections such as LSH. However, improvements occur only for relatively small hash code sizes up to 64 or 128 bits. As discussed in the paper, this is mainly due to the lack of independence between the produced hash functions. We introduce a new hash function family that attempts to solve this issue in any kernel space. Rather than boosting the collision probability of close points, our method focus on data scattering. By training purely random splits of the data, regardless the closeness of the training samples, it is indeed possible to generate consistently more independent hash functions. On the other side, the use of large margin classifiers allows to maintain good generalization performances. Experiments show that our new Random Maximum Margin Hashing scheme (RMMH) outperforms four state-of-the-art hashing methods, notably in kernel spaces.