A method of avoiding damage to a decoupling hose mounted between two tubes of a motor vehicle exhaust system, said hose comprising a deformable inner portion, an outer sealing leakproofing portion in the form of a continuous and leaktight sleeve having a flexible central zone and two rigid endpieces, and an intermediate portion in the form of a wad of thermal lagging extending substantially over the entire length of the outer sleeve, each rigid endpiece extending at least over a length such that its peripheral end edge connected to the flexible central zone overlies the inner portion of the hose which is subjected to deformation, wherein, in order to avoid any damage to the wad of thermal lagging by said peripheral end edge of each endpiece, the method consists in defining the effective length of the endpieces in such a manner that for the wad of thermal lagging having an initial thickness H0 and a compressed thickness Hc when compressed by said peripheral edge of each endpiece during maximum transverse deflection in operation of the inner portion of the hose, the ratio [H0-Hc]/H0 is less than 0.3.