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· 10 34 cm− 2 s− 1. The region of the forward muon spectrometer (| η|> 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 Butler et al.(2015). The design of small size prototypes and the studies of their performances under high rate particles flux is presented.