International audienceThe M dwarf GJ 436 hosts a transiting warm Neptune known to experience atmospheric escape. Previous observations revealed the presence of a giant hydrogen exosphere transiting the star for more than 5 h, and absorbing up to 56% of the flux in the blue wing of the stellar Lyman-α line of neutral hydrogen (H I Lyα). The unexpected size of this comet-like exosphere prevented observing the full transit of its tail. In this Letter, we present new Lyα observations of GJ 436 obtained with the Space Telescope Imaging Spectrograph (STIS) instrument onboard the Hubble Space Telescope. The stability of the Lyα line over six years allowed us to combine these new observations with archival data sets, substantially expanding the cov...