  The 50~kton Iron Calorimeter (ICAL) detector at the underground India based
Neutrino Observatory (INO) will make measurements on atmospheric neutrinos.
Muons produced in charged current (CC) interactions of muon neutrinos with the
iron are tracked spatially and temporally through the signals that they produce
in the Resistive Plate Chambers~(RPCs) that are interleaved with iron layers.
Since the RPCs will be operated in the avalanche mode the signal rise-time is
$\sim~1~\rm{nsec}$ resulting in a fast time response. While the muon track is
derived from the X and Y hit information of the RPCs and the layer number (Z),
the upward or downward direction is obtained by using the time information from
the detector. Such a capability can be examined by analysing the timing
information from $1~\rm{m}~\times~1~\rm{m}$ glass RPCs, with $3~\rm{cm}$ wide
X- and Y- pick-up strips, in a $12$ layer RPC stack that measures cosmic muon
events. The present study looks at the pixel-wise time response of these RPCs
in order to improve the relative time distribution and hence the up-down
discrimination capability. After including the effect of propagation delay in
the cable and pick-up panel the time resolution improves, in some cases, to
$\leq~1~\rm{nsec}$ whereas in some cases there is no significant change. These
results will help in significantly improving on the extraction of the
directionality of muons produced in CC interactions of $\nu_{\mu}$ and
$\bar{\nu}_{\mu}$.
