A gas detector with parallel resistive electrodes has intrinsic capability of efficient detection at high particle fluxes. An inverted Double Gap Resistive Plate Chamber made of special bakelite of low resistivity −ρ=5·108Ωcm, reaches full efficiency with a plateau exceeding 500V for radiation rates as high as 7kHz/cm2 measured with a periodic beam. A gas mixture containing a majority of so called “green freon” – C2H2F4 assures stable avalanche amplification with a time resolution of about 2ns, only slightly dependent on the particle flux.Measurements with a strong 137Cs source confirm stability of parameters in continuous radiation flux up to 5kHz/cm2/gap. The results demonstrate the usefulness of an RPC as a muon trigger detector in a high radiation background environment, expected in the CMS experiment in the highest rapidity region.