Heart rate asymmetry is an unequal and unidirectional phenomenon where the contribution of heart rate decelerations to short-term heart rate variability is greater than that of accelerations, and the contribution of accelerations to long-term and total variability is greater than that of deceleration. This has been established for short, stationary recordings. In this paper, we analyse heart rate asymmetry in 87 long, 24-hour ECG Holter recordings from healthy people. We show that in the whole recording all types of asymmetry are observable, clear and highly statistically significant. To analyse the local changes of asymmetry in time, we analyzed the recordings by disjoint jumping windows of 300-beats. This analysis revealed that also the local, averaged measures of all types of asymmetry demonstrate its presence which is highly statistically significant. Additionally, we introduce in this paper a statistical test for asymmetry in the single long recording, as opposed to the current approach in which the whole groups are tested. We do so by introducing the proportion of time spent in asymmetry for each recording and using it in the binomial tests. We found that for all the recordings most of the time is spent in asymmetry.