  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.
