We propose a novel decomposition method for electromyographic signals based on blind source separation. Using the cyclostationary properties of motor unit action potential trains (MUAPt), it is shown that the MUAPt can be decomposed by joint diagonalization of the cyclic spatial correlation matrix of the observations. After modeling the source signals, we provide the proof of orthogonality of the sources and of their delayed versions in a cyclostationary context. We tested the proposed method on simulated signals and showed that it can decompose up to six sources with a probability of correct detection and classification >95%, using only eight recording sites. Moreover, we tested the method on experimental multi-channel signals recorded with thin-film intramuscular electrodes, with a total of 32 recording sites. The rate of agreement of the decomposed MUAPt with those obtained by an expert using a validated tool for decomposition was >93%.