  The HL-LHC phase is designed to increase by an order of magnitude the amount
of data to be collected by the LHC experiments. To achieve this goal in a
reasonable time scale the instantaneous luminosity would also increase by an
order of magnitude up to $6 \cdot 10^{34}$ cm$^{-2}$s$^{-1}$. The region of the
forward muon spectrometer ($|\eta| > 1.6$) is not equipped with RPC stations.
The increase of the expected particles rate up to 2 kHz/cm$^2$ ( including a
safety factor 3 ) motivates the installation of RPC chambers to guarantee
redundancy with the CSC chambers already present. The actual RPC technology of
CMS cannot sustain the expected background level. A new generation Glass-RPC
(GRPC) using low resistivity glass (LR) is proposed to equip at least the two
most far away of the four high eta muon stations of CMS. The design of small
size prototypes and the studies of their performances under high rate particles
flux is presented.
