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Within the framework of the unmixing of hyperspectral images, the pixel mixture is a difficult problem to solve. This difficulty comes from several outliers which seriously affect the reliability of spectral unmixing results. The illumination change effect, where the image does not reflect the true appearance of the scene, in many cases due to shadow facts, is considered to be one of the most important outliers. The present work proposes a new approach called Spectral Angle Measure-based Spectral Unmixing which uses the spectral angle constraint for abundance quantification. The major benefit of this approach is its ability to take advantage of the geometric properties of the Spectral Angle Measure technique to estimate abundance quantification independently of the amplitude (magnitude) of the Endmembers spectral signatures, using only spectral angle measures. As a consequence, a significant reduction in spectral unmixed error corresponding to the spectral similarity within-class confusion is obtained. A second benefit concerns physical constraints which are respected. The experiment was conducted using simulated and real images to validate our approach and to compare it with a well known statistical one.