Glaucoma is the second leading cause of blindness worldwide. It is a disease in which fluid pressure in the eye increases continuously, damaging the optic nerve and causing vision loss. Computational decision support systems for the early detection of glaucoma can help prevent this complication. The retinal optic nerve fiber layer can be assessed using optical coherence tomography, scanning laser polarimetry, and Heidelberg retina tomography scanning methods. In this paper, we present a novel method for glaucoma detection using a combination of texture and higher order spectra (HOS) features from digital fundus images. Support vector machine, sequential minimal optimization, naive Bayesian, and random-forest classifiers are used to perform supervised classification. Our results demonstrate that the texture and HOS features after z-score normalization and feature selection, and when combined with a random-forest classifier, performs better than the other classifiers and correctly identifies the glaucoma images with an accuracy of more than 91%. The impact of feature ranking and normalization is also studied to improve results. Our proposed novel features are clinically significant and can be used to detect glaucoma accurately.