Heart rate asymmetry (HRA) is considered as a physiological phenomenon in healthy subjects. In this article, we propose a novel HRA index, Slope Index (SI), to quantify phase asymmetry of heart rate variability (HRV) system. We assessed the performance of proposed index in comparison with conventional (Guzik's Index (GI) and Porta's Index (PI)) HRA indices. As illustrative examples, we used two case studies: (i) differentiate physiologic RR series from synthetic RR series; and (ii) discriminate arrhythmia subjects from Healthy using beat-to-beat heart rate time series. The results showed that SI is a superior parameter than GI and PI for both case studies with maximum ROC area of 0.84 and 0.82 respectively. In contrast, GI and PI had ROC areas {0.78, 0.61} and {0.50, 0.56} in two case studies respectively. We also performed surrogate analysis to show that phase asymmetry is caused by a physiologic phenomena rather than a random nature of the signal. In conclusion, quantification of phase asymmetry of HRV provides additional information on HRA, which might have a potential clinical use to discriminate pathological HRV in future.