The diagnosis of late onset sepsis in premature infants remains difficult because clinical signs are subtle and non-specific and none of the laboratory tests, including CRP and blood culture, have high predictive accuracy. Heart rate variability (HRV) analysis emerges as a promising diagnostic tool. Entropy and long-range fractal correlation are decreased in premature infants with proven sepsis. Besides this, respiration and its relations to HRV appear to be less. The objective of this study was to determine if analysis of time-frequency correlations between the heart rate and respiration amplitude may help for the diagnosis of infection in premature infants. An estimator of the linear relationship between nonstationary signals, recently introduced, is explored. The tests were performed on a cohort study of 60 premature infants. The results show that the correlation in the low frequency band tended to be higher in the sepsis group.