This paper presents a successive stream selection algorithm applied to the interference channel. The proposed solution consists in a stream-wise stream selection procedure. At each recursion, the selection is done in the null space of both VTC and VRC of the previously selected streams. This ensures to cancel the interference terms and offers a practical interference alignment solution without consideration of the feasibility conditions. Thus, the obtained solutions constructs the precoding and decoding vectors to be used for the different communicating users with the optimal number of admissible streams for the considered system. Fairness between users is respected on average as the per user mean achieved number of streams is greater than those offered by an interference alignment solution.