Despite the significant experimental effort made in the last decades, the origin of the ultra high energy cosmic rays is still unknown. The chemical composition of these energetic particles carries key astrophysical information to identify where they come from. It is well known that the muon content of the showers generated by the interaction of the cosmic rays with air molecules, is very sensitive to the primary particle type. Therefore, the measurement of the number of muons at ground level is an essential tool to infer the cosmic ray mass composition. We introduce a novel method to reconstruct the lateral distribution of muons with an array of counters buried underground like AMIGA, one of the Pierre Auger Observatory detector systems. The reconstruction builds on a previous method we recently presented by considering the detector time resolution. With the new method more events can be reconstructed than with the previous one. In addition the statistical uncertainty of the measured number of muons is reduced, allowing for a better primary mass discrimination.
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