In this letter, we advocate that it is possible to mitigate Pilot Contamination in Massive MIMO systems by scrambling the pilot sequences with a Base Station (BS) scrambling sequence. It is possible if a set of sequences is carefully designed to meet the orthogonality property defined in this letter. Each BS possesses its own scrambling sequence that can be reused the same way frequency reuse is applied to cell deployment. The main advantage of the prosed pilot generation scheme is that the frequency reuse factor can be set to 1, the most aggressive one, while the scrambling sequences can be reused with much less aggressive reuse factors (e.g. 4, 7, 9, 12, etc.), which in consequence results in pilot contamination mitigation and increased system's performance.