For the specific analysis of the variability of RR intervals of the cardiac rhythm, a method for measuring the instantaneous cardiac rhythm (ICR) represented by a multifractal dynamical model (MDM) has been developed. The advantages of this method, compared to the statistical methods of analysis of the RR intervals used, have been demonstrated. The method allows possible catastrophes of the cardiovascular system to be predicted. Using the data of Holter monitoring and the program system developed, we have plotted ICR curves, an ICR piecewise linear trend, and variability charts for three randomly chosen time intervals. The self-similarity (fractality) of the ICR up to an accuracy of 5% has been shown based on the explicit data. The MDM parameters have been calculated based on the ICR data. The analysis of the dynamics of these parameters has been conducted and their compliance with the status of the patient examined has been studied. The relevance of the ICR examination within MDM is closely related to the necessity of recognizing new markers of adverse cardiovascular episodes. The research performed shows that the results obtained could be taken as a basis for developing a new mathematical method of ICR examination based on Holter monitoring.