Heart rate variability (HRV) has successfully predicted health outcomes in the adult. Similar data related to the neonate is lacking. The study objective was to quantify the HRV as to health status in 13 maturing preterm neonates measured weekly from 26-35 weeks post-conceptional age (PCA). Inclusion criteria were appropriateness for gestational age, no congenital anomalies, an intraventricular hemorrhage ≤ grade 2, no substance abuse exposure and no vasopressors. The 10-minute data collection period consisted of capturing the heart rate by connecting a 3-lead ECG to a ECG-Preamplifier, digitizing the signal at 250 Hertz. At 35 weeks PCA the neonates were classified as healthy(tolerating full feeds and requiring no respiratory support) or compromised(requiring respiratory support). Dispersional analysis, a method of quantifying the autocorrelation in a data set by estimating its fractal dimension (FD), was used to describe HRV. We found that the FD has no significant dependence on health status or PCA. The FD is typically about 1.5, which implies that there is little short-range autocorrelation in the interbeat period fluctuations. Zbilut, Zak, and Webber (1994) report a similar result for the healthy human adult male, which also shows little short-term autocorrelation in the interbeat interval changes. Therefore, the fluctuations in the periods between beats are usually largely independent of the fluctuations in the intervals between previous heartbeats for preterm neonates as well as adults.