Exhaust line for an internal combustion engine exhaust arrangement with a catalytic converter, which exhaust line, as viewed in a flow direction of an exhaust gas from an internal combustion engine, located upstream of the catalytic converter, adjacent to the engine, and the exhaust line having an externally located heat-conducting layer comprising a metallic material and a beat-insulating material layer internally located on the heat conducting layer, the heat-insulating layer and the heat-conducting layer being connected forcewise with another, wherein the heat-insulating layer and the heat-conducting layer are directly connected with one another, the heat-insulating layer is located inwardly of the exhaust line, the heat-insulating layer with a predetermined layer thickness is arranged to be in direct contact with the exhaust gas, the heat-insulating layer is configured to include a plurality of thin areas having a thickness reduced by at least about 10% from the predetermined layer thickness to less than about 2 mm, whereby the thermal conductivity of the heat-insulating layer is less than about 106 J/(m3h), and the thermal diffusivity of the heat-insulating layer is sized to be less than about 0,01 cm2/s.