Objective- This study aims to develop a novel framework for high-density surface electromyography (HD-sEMG) signal decomposition with superior decomposition yield and accuracy, especially for low-energy MUs. Methods- An iterative convolution kernel compensation-peel off (ICKC-P) framework is proposed, which consists of three steps: decomposition of the motor units (MUs) with relatively large energy by using the iterative convolution kernel compensation (ICKC) method and extraction of low-energy MUs with a Post-Processor and novel 'peel-off' strategy. Results- The performance of the proposed framework was evaluated by both simulated and experimental HD-sEMG signals. Our simulation results demonstrated that, with 120 simulated MUs, the proposed framework extracts more MUs compared to K-means convolutional kernel compensation (KmCKC) approach across six noise levels. And the proposed 'peel-off' strategy estimates more accurate MUAP waveforms at six noise levels than the 'peel-off' strategy proposed in the progressive FastICA peel-off (PFP) framework. For the experimental sEMG signals recorded from biceps brachii, an average of 16.1 ±3.4 MUs were identified from each contraction, while only 10.0 ± 2.8 MUs were acquired by the KmCKC method. Conclusion- The high yield and accuracy of MUs decomposed from simulated and experimental HD-sEMG signals demonstrate the superiority of the proposed framework in decomposing low-energy MUs compared to existing methods for HD-sEMG signal decomposition. Significance- The proposed framework enables us to construct a more representative motor unit pool, consequently enhancing our understanding pertaining to various neuropathological conditions and providing invaluable information for the diagnosis and treatment of neuromuscular disorders and motor neuron diseases.