Congestive heart failure (CHF) is a major medical challenge in developed countries. In order to screen patients with CHF and healthy subjects during circadian observation, accurate judgment and fast response are imperative. In this study, optimal timing during circadian observation via the heart rate variability (HRV) was sought. We tested 29 CHF patients and 54 healthy subjects in the control group from the interbeat interval databases of PhysioBank. By invoking the alpha1 parameter in detrended fluctuation analysis of HRV, we found that it could be used as an indicator to screen the patients with CHF and subjects in normal sinus rhythm (NSR) under Kruskal-Wallis test. By invoking Fano factor, the optimal timing to screen CHF patients and healthy subjects was found to be from 7 PM to 9 PM during the circadian observation. In addition, this result is robust in a sense that the same result can be achieved by using different ECG recording lengths of 2, 5, 10, ... , and 120 min, respectively. Furthermore, a support vector machine was employed to classify CHF and NSR with alpha1 parameter of a moving half-hour ECG recordings via leave-one-out cross validation. The results showed that the superlative screening performance was obtained in the 7 pm-9 pm period during circadian observation. It is believed that this result of optimal timing will be helpful in the non-invasive monitoring and screening of CHF patients and healthy subjects in the clinical practice.