Different measures of heart rate variability and particularly of respiratory sinus arrhythmia are widely used in research and clinical applications. Inspired by the ideas from the theory of coupled oscillators, we use simultaneous measurements of respiratory and cardiac activity to perform a nonlinear decomposition of the heart rate variability into the respiratory-related component and the rest. We suggest to exploit the technique as a universal preprocessing tool, both for the analysis of respiratory influence on the heart rate as well as in cases when effects of other factors on the heart rate variability are in focus. The theoretical consideration is illustrated by the analysis of 25 data sets from healthy subjects.