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This letter proposes a linear two-class hyperspectral pixel-unmixing algorithm that uses a band selection method to determine the best bands for pixel unmixing, low-pass prefiltering to remove high-frequency content, and a new version of the well-known singular value decomposition (SVD) method, which is insensitive to dc offsets (DCI-SVD). The proposed method is compared to the best level discrete wavelet transform approach for dimensionality reduction and least squares estimation and quadratic programming for unmixing (DWT-LSE-QP). The contributions of this letter are given as follows: (1) the band selection and filter selection algorithm and (2) the DCI-SVD algorithm. The dc insensitivity of the DCI-SVD method is proven, and simulation results using data from an analytical spectral device spectroradiometer show the efficacy of the proposed method and its superiority to the DWT-LSE-QP-based approach in the harder unmixing cases.