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This study presents a novel high density surface electromyography (EMG) decomposition method, named as 2CFastICA, because it incorporates two key algorithms: kernel constrained FastICA and correlation constrained FastICA. The former focuses on overcoming the local convergence of FastICA without requiring the peel-off strategy used in the progressive FastICA peel-off (PFP) framework. The latter further refines the output of kernel constrained FastICA by correcting possible erroneous or missed spikes. The two constrained FastICA algorithms supplement each other to warrant the decomposition performance. The 2CFastICA method was validated using simulated surface EMG signals with different motor unit numbers and signal to noise ratios (SNRs). Two source validation was also performed by simultaneous high density surface EMG and intramuscular EMG recordings, showing a matching rate (MR) of (97.2 ± 3.5)% for 170 common motor units. In addition, a different form of two source validation was also conducted taking advantages of the high density surface EMG characteristics of patients with amyotrophic lateral sclerosis, showing a MR of (99.4 ± 0.9)% for 34 common motor units from interference and sparse datasets. Both simulation and experimental results indicate that 2CFastICA can achieve similar decomposition performance to PFP. However, the efficiency of decomposition can be greatly improved by 2CFastICA since the complex signal processing procedures associated with the peel-off strategy are not required any more. Along with this paper, we also provide the MATLAB open source code of 2CFastICA for high density surface EMG decomposition.