Objective : Spike sorting of muscular and neural recordings requires separating action potentials that overlap in time (superimposed action potentials (APs)). We propose a new algorithm for resolving superimposed action potentials, and we test it on intramuscular EMG (iEMG) and intracortical recordings. Methods : Discrete-time shifts of the involved APs are first selected based on a heuristic extension of the peel-off algorithm. Then, the time shifts that provide the minimal residual Euclidean norm are identified (Discrete Brute force Correlation (DBC)). The optimal continuous-time shifts are then estimated (High-Resolution BC (HRBC)). In Fusion HRBC (FHRBC), two other cost functions are used. A parallel implementation of the DBC and HRBC algorithms was developed. The performance of the algorithms was assessed on 11,000 simulated iEMG and 14,000 neural recording superpositions, including two to eight APs, and eight experimental iEMG signals containing four to eleven active motor units. The performance of the proposed algorithms was compared with that of the Branch-and-Bound (BB) algorithm using the Rank-Product (RP) method in terms of accuracy and efficiency. Results : The average accuracy of the DBC, HRBC and FHRBC methods on the entire simulated datasets was 92.16±17.70, 93.65±16.89, and 94.90±15.15 (%). The DBC algorithm outperformed the other algorithms based on the RP method. The average accuracy and running time of the DBC algorithm on 10.5 ms superimposed spikes of the experimental signals were 92.1±21.7 (%) and 2.3±15.3 (ms). Conclusion and Significance : The proposed algorithm is promising for real-time neural decoding, a central problem in neural and muscular decoding and interfacing.