A novel approach to distinguish congestive heart failure (CHF) subjects from healthy subjects is proposed. Heart rate variability (HRV) is impaired in CHF subjects. In this work hypothesizing that capturing moment to moment nonlinear dynamics of HRV will reveal cardiac patterning, we construct the nonlinear scatter plot for Teager energy of R-R interval series. The key feature of Teager energy is that it models the energy of the source that generated the signal rather than the energy of the signal itself. Hence, any deviations in the genesis of HRV, by complex interactions of hemodynamic, electrophysiological, and humoral variables, as well as by the autonomic and central nervous regulations, get manifested in the Teager energy function. Comparison of the Teager energy scatter plot with the second-order difference plot (SODP) for normal and CHF subjects reveals significant differences qualitatively and quantitatively. We introduce the concept of curvilinearity for central tendency measures of the plots and define a radial distance index that reveals the efficacy of the Teager energy scatter plot over SODP in separating CHF subjects from healthy subjects. The k-nearest neighbor classifier with RDI as feature showed almost 100% classification rate.