  In CBM Experiment at FAIR, dimuons will be detected by a Muon Chamber (MUCH)
consisting of segmented absorbers of varying widths and tracking chambers
sandwiched between the absorber-pairs. In this fixed target heavy-ion collision
experiment, operating at highest interaction rate of $10~MHz$ for $Au+Au$
collision, after the first MUCH detector station in its inner radial ring will
face a particle rate of $1~MHz/cm^2$. To operate at such a high particle
density, GEM technology based detectors have been selected for the first two
stations of MUCH. We have reported earlier the performance of several
small-size GEM detector prototypes built at VECC for use in MUCH. In this work,
we report on a large GEM chamber prototype tested with proton beam of momentum
$2.36~GeV/c$ at COSY-J\"{u}elich Germany. The detector was read out using
nXYTER ASIC operated in self-triggering mode. An efficiency higher than $96\%$
at $\Delta V_{GEM}~=~375.2~V$ was achieved. The variation of efficiency with
the rate of incoming protons has been found to vary within $2\%$ when tested up
to a maximum rate of $2.8~MHz/cm^2$. The gain was found to be stable at high
particle rate with a maximum variation of $\sim~9\%$.
