We present a constrained spectral unmixing method to remove highlight from a single spectral image. In the constrained spectral unmixing method, the constraints have been imposed so that all the fractions of diffuse and highlight reflection sum up to 1 and are positive. As a result, the spectra of the diffuse image are always positive. The spectral power distribution (SPD) of the light source has been used as the pure highlight spectrum. The pure diffuse spectrum of the measured spectrum has been chosen from the set of diffuse spectra. The pure diffuse spectrum has a minimum angle among the angles calculated between spectra from a set of diffuse spectra and the measured spectrum projected onto the subspace orthogonal to the SPD of the light source. The set of diffuse spectra has been collected by an automated target generation program from the diffuse part in the image. Constrained energy minimization in a finite impulse response linear filter has been used to detect the highlight and diffuse parts in the image. Results by constrained spectral unmixing have been compared with results by the orthogonal subspace projection (OSP) method [Proceedings of International Conference on Pattern Recognition (2006), pp. 812-815] and probabilistic principal component analysis (PPCA) [Proceedings of the 4th WSEAS International Conference on Signal Processing, Robotics and Automation (2005), paper 15]. Constrained spectral unmixing outperforms OSP and PPCA in the visual assessment of the diffuse results. The highlight removal method by constrained spectral unmixing is suitable for spectral images.