The paper studies a surface electromyogram (SEMG) decomposition technique suitable for identification of complete motor unit (MU) firing patterns and their motor unit action potentials (MUAPs) during low-level isometric voluntary muscle contractions. The algorithm was based on a correlation matrix of measurements, assumed unsynchronised (uncorrelated) MU firings, exhibited a very low computational complexity and resolved the superimposition of MUAPs. A separation index was defined that identified the time instants of an MU's activation and was eventually used for reconstruction of a complete MU innervation pulse train. In contrast with other decomposition techniques, the proposed approach worked well also when the number of active MUs was slightly underestimated, if the MU firing patterns partly overlapped and if the measurements were noisy. The results on synthetic SEMG show 100% accuracy in the detection of innervation pulses down to a signal-to-noise ratio (SNR) of 10 dB, and 93±4.6% (mean± standard deviation) accuracy with 0 dB additive noise. In the case of real SEMG, recorded with an array of 61 electrodes from biceps brachii of five subjects at 10% maximum voluntary contraction, seven active MUs with a mean firing rate of 14.1 Hz were identified on average.