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 middot 10 super(34) cm super(-2)s super(-1). The region of the forward muon spectrometer (eta > 1.6) is not equipped with RPC stations. The increase of the expected particles flux up to 2 kHz/cm super(2) (including a safety factor 3) motivates the installation of RPC chambers to guarantee redundancy with the CSC chambers already present. The current CMS RPC technology cannot sustain the expected background level. The new technology that will be chosen should have a high rate capability and provide a good spatial and timing resolution. A new generation of Glass-RPC (GRPC) using low-resistivity glass is proposed to equip at least the two most far away of the four high eta muon stations of CMS. First the design of small size prototypes and studies of their performance in high-rate particles flux are presented. Then the proposed designs for large size chambers and their fast-timing electronic readout are examined and preliminary results are provided.