The h-index is the most used measurement of impact for researchers. Sites such as Web of Science, Google Scholar, Microsoft Academic, and Scopus leverage it to show and compare the impact of authors. The h-index can be described in simple terms: it is the highest h for which an authors has h papers with the number of cites more or equal than h. Unfortunately, some researchers, in order to increase their productivity artificially, manipulate their h-index using different techniques such as self-citation. Even though it is relatively simple to discard self-citations, every day appears more sophisticated methods to artificially increase this index. One of these methods is collaborative citations, in which a researcher A cites indiscriminately another researcher B, with whom it has a previous collaboration, increasing her/his h-index. This work presents a new robust generalization of the h-index called rh-index that minimizes the impact of new collaborative citations, maintaining the importance of their citations previous to their collaborative work. To demonstrate the usefulness of the proposed index, we analyze its effect over 600 Chilean researchers. Our results show that, while some of the most cited researchers were barely affected, demonstrating their robustness, another group of authors show a substantial reduction in comparison to their original h-index.