In general, the first overtone modes produce weak bands that appear at approximately twice the wavenumber value of the fundamental transitions in vibrational spectra. Here, we report the existence of a series of enhanced non-fundamental bands in resonance Raman (RR) spectra recorded for hemoglobin (Hb) inside the highly concentrated heme environment of the red blood cell (RBC) by exciting with a 514.5 nm laser line. Such bands are most intense when detecting parallel-polarized light. The enhancement is explained through excitonic theory invoking a type C scattering mechanism and bands have been assigned to overtone and combination bands based on symmetry arguments and polarization measurements. By using malaria diagnosis as an example, we demonstrate that combining the non-fundamental and fundamental regions of the RR spectrum improves the sensitivity and diagnostic capability of the technique. The discovery will have considerable implications for the ongoing development of Raman spectroscopy for blood disease diagnoses and monitoring heme perturbation in response to environmental stimuli.