PageRank is defined as the stationary state of a Markov chain depending on a damping factor that spreads uniformly part of the rank. The choice of is eminently empirical, and in most cases the original suggestion = 0.85 by Brin and Page is still used. It is common belief that values of closer to 1 give a "truer to the web" PageRank, but a small accelerates convergence. Recently, however, it has been shown that when = 1 all pages in the core component are very likely to have rank 0 [1]. This behaviour makes it difficult to understand PageRank when 1, as it converges to a meaningless value for most pages. We propose a simple and natural modification to the standard preprocessing performed on the adjacency matrix of the graph, resulting in a ranking scheme we call TruRank. TruRank ranks the web with principles almost identical