We present a new analysis of the far-IR emission at high Galactic latitude based on COBE and HI data .
A decomposition of the Far-IR emission over the HI , H ^ { + } and H _ { 2 } Galactic gas components and the Cosmic Far InfraRed Background ( CFIRB ) is described .

For the first time the far-IR emission of dust associated with the Warm Ionised Medium ( WIM ) is evidenced .
This component determined on about 25 \% of the sky is detected at a 10 \sigma level in the [ 200 , 350 ] { \mu m } band .
The best representation of the WIM dust spectrum is obtained for a temperature of 29.1 K and an emissivity law \tau / N _ { H } ^ { + } = 3.8 \pm 0.8 10 ^ { -26 } ~ { } ( \lambda / 250 { \mu m } ) ^ { -1 } cm ^ { 2 } .
With a spectral index equal to 2 , the emissivity law becomes \tau / N _ { H } ^ { + } = 1.0 \pm 0.2 10 ^ { -25 } ~ { } ( \lambda / 250 { \mu m } ) ^ { -2 } cm ^ { 2 } , with a temperature of 20 K , which is significantly higher than the temperature of dust associated with HI gas .
The variation in the dust spectrum from the HI to the WIM component can be explained by only changing the upper cutoff of the Big Grain size distribution from 0.1 { \mu m } to 30 nm . The detection of IR emission of dust in the WIM significantly decreases the intensity of the CFIRB , especially around 200 { \mu m } which corresponds to the peak of energy .