A new index for the analysis of the heart rate variability (HRV) dynamics is presented. The proposed index (acceleration change index (ACI)) characterizes the sign of the differences of a time series. A theoretical study shows an expression that relates ACI and the autocorrelation function of the time series. This formula is tested and validated with different simulated time series (uncorrelated noise, sinusoidal and fractional Brownian motion). Next, ACI is applied to RR time series from healthy subjects showing that ACI decreases with periodic controlled breathing, increases during exercise, and it has a lower value at night than during the day. In a preliminary study, ACI has been shown to be lower in healthy subjects than in patients who had suffered a myocardial infarction one month previously. ACI can be employed as a fast and robust new marker of the HRV dynamics.