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HRTF databases available today offer different sampling schemes. These schemes differ in the number of arrival angles and in the distribution of the angles. To evaluate the pressure at the ears at intermediate arrival angles not sampled in the database, interpolation is required. In addition to the limited spatial resolution, most databases lack measurements below certain elevation angles, since sound rarely arrives from directly below the listener and due to technical constraints in the measurement system. This lack of measurement positions introduces errors to the interpolation process. Different methods proposed to reduce the error include diagonal loading (DL) and methods for robust matrix inversion. In this work a method is proposed for interpolating HRTF utilizing singular-value decomposition (SVD). Considering only the significant singular vectors holding most of the energy of the HRTFs, an algebraic manipulation defines a new set of base functions. This set holds low energy levels at directions where no measurements were taken, and favors the signal space over the null space. Interpolation performed using this new set is more natural to the sampling scheme and produces a lower average error rate. The error at different frequencies is compared to other methods such as traditional Spherical Harmonics Decomposition using DL.