This paper presents a successive stream selection algorithm than can be used for the interference channel. The proposed solution is a stream-wise construction of the precoding and decoding vector sets. These beams are selected to minimize the interference between the selected streams based on the projections of the nominal directions derived via SVD. The projections are made such that the obtained new stream is in both null spaces of the receiving and transmitting directions of all previously selected streams. This means that it interferes the least with the other selected streams and is also weakly interfered by them.