Global-scale assessment of burned area (BA) is essential for climate studies and open access satellite-borne multispectral (MS) imagery is vital for the mapping purpose. Global characterization of BAs via MS analysis is difficult as it usually requires ancillary data to model local factors such as vegetation types and local ecoclimate systems. This article proposes a novel classification model that exploits certain mathematical properties of normalized difference indexes (NDIs) to build an abstract space of features where the BA class can be learned globally and solely using MS images. The core idea is that, although NDIs are subject to strong intraclass variations, their mutual order (i.e., the sign of their difference) can be robust enough for characterization. By encoding every possible such ordering relation in a binary domain, the feature space turns out to be hyperdimensional, with abstraction capabilities similar to that of neural network (NN) layers. The proposed classification model is one-class and, therefore, is very convenient as it only requires training samples for the positive class to be collected. The model is experimentally validated in an extensive BA detection exercise with Sentinel-2 images that involves recently published global BA reference data. Results are promising as we report higher -score than those reported for state-of-the-art BA products currently available, which are obtained through hybrid techniques and multiple data sources. The model also outperforms the well-known and largely used one-class support vector machine (OC-SVM), which is tested in this work for the first time for BA detection at a global scale.