Heart rate variability (HRV) plays an important role in medicine and psychology because it is used to quantify imbalances of the autonomic nervous system (ANS). An important manifestations of the ANS on HRV is also directly related to respiration and it is called respiratory sinus arrhythmia (RSA). This is a controlled phenomenon that leads to a synchronized coupling between respiration and instantaneous heart rate. Thus, the portion of HRV that is not related to respiration, and could potentially contain undiscovered diagnostic value, is overlapped and remains hidden in a standard HRV analysis. In such cases, a decoupling procedure would deliver a discriminated HRV analysis and possible new insights about the regulation of the cardiovascular system. In this work, we propose an algorithm based on Granger's causality to measure coupling between respiration and HRV. In the case of significant coupling, we estimate and cancel the respiration driven HRV component using a linear filtering approach. We tested the method using synthetic signals and prove it to deliver a reliable coupling measurement in 96.3% of the cases and reconstruct respiration free signals with a median correlation coefficient of 0.992. Afterwards, we applied our method to signals recorded during paced respiration and during natural breathing. We demonstrated that coupling is dependent on respiratory frequency and that it maximizes at 0.3 Hz. Furthermore, the HRV parameters measured during paced respiration tend to level among subjects after decoupling. The intersubject variability of HRV parameter is also decreased after the separation process. During natural breathing, coupling is notoriously lower to non-existing and decoupling has little impact on HRV. We conclude that the method proposed here can be used to investigate the diagnostic value of respiration independent HRV parameters.