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We develop a data-adaptive dimension reduction algorithm that is robust against out-of-sector sources in application to array processing. The dimension reduction is done as a linear transformation (matrix filter). The matrix filter is designed adaptively such that the signal power within a certain sector is preserved while the out-of-sector power is maximally rejected. The columns of the beamspace matrix are designed sequentially, one column at a time. This sequential implementation is carried out by imposing orthogonality constraints between beamspace matrix columns. Hence, the white noise property at the output of the beamspace preprocessor is preserved. The latter is important for subsequent data processing. The proposed algorithm is computationally less expensive as compared to the existing data-adaptive beamspace design techniques. Simulation results validate the robustness of the developed algorithm, and they show its effectiveness and superiority to the existing algorithms.