Abstract: Novel atom-based molecular descriptors based on a bilinear map similar to use defined in linear algebra are presented. These molecular descriptors, called “local (atom, group and atom-type) and total (global) bilinear indices”, are proposed here as a new molecular parametrization easily calculated from the 2D molecular information. The proposed non-stochastic and stochastic molecular fingerprints try to match molecular structure provided by the molecular topology by using the kth non-stochatic (Marrero-Ponce, Y. J. Chem. Inf. Comput. Sci. 2004, 44, 2010 and Marrero-Ponce, Y. Molecules 2003, 8, 687) and stochastic (Marrero-Ponce, Y., et al. J. Mol. Struc. (Theochem) 2005, 717, 67 and Marrero-Ponce, Y.; Castillo-Garit, J. A. J. Comput.-Aided Mol. Des. DOI: DO00017575) graph–theoretic electronic-density matrices, Mk and Sk, respectively. That is to say, the kth non-stochastic and stochastic bilinear indices are calculated using Mk and Sk as matrix operators of bilinear transformations. Moreover, chemical information is codified by using different pair combinations of atomic weightings (atomic mass, polarizability, van der Waals volume, and electronegativity). The prediction ability in Quantitative Structure-Property Relationships (QSPR) of the new molecular descriptors was tested by analysing regressions of these descriptors for six selected properties of octane isomers. It was clearly demonstrated that prediction ability was higher than those showed by other 2D/3D well-known sets of molecular descriptors. The obtained results suggest that with the present method it is possible to obtain a good estimation of these physicochemical properties for octanes. The approach described in the present report appears to be a prominent method to find quantitative models for description of physicochemical and biological properties.