This paper presents a novel signal compression algorithm based on the Blaschke unwinding adaptive Fourier decomposition (AFD). The Blaschke unwinding AFD is a newly developed signal decomposition theory. It utilizes the Nevanlinna factorization and the maximal selection principle in each decomposition step, and achieves a faster convergence rate with higher fidelity. The proposed compression algorithm is applied to the electrocardiogram signal. To assess the performance of the proposed compression algorithm, in addition to the generic assessment criteria, we consider the less discussed criteria related to the clinical needs - for the heart rate variability analysis purpose, how accurate the R-peak information is preserved is evaluated. The experiments are conducted on the MIT-BIH arrhythmia benchmark database. The results show that the proposed algorithm performs better than other state-of-the-art approaches. Meanwhile, it also well preserves the R-peak information.