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In this paper, we develop an algorithm for data-adaptive beamspace preprocessing with robustness against out-of-sector sources. Our algorithm yields an orthogonal beamspace matrix and, hence, it preserves the white noise property at the output of the beamspace preprocessor. The beamspace matrix is designed as a matrix filter that maintains an almost distortionless response towards sources within the beamspace sector while maximally rejects all out-of-sector sources. The columns of the beamspace matrix are designed sequentially, one column at a time. This sequential implementation is curried out by imposing orthogonality constraints between beamspace matrix columns. The proposed algorithm is computationally less expensive as compared to the existing data-adaptive beamspace design techniques. Simulation results are provided to validate the robustness of the developed algorithm, and show its effectiveness.