The nearby transiting system GJ 436b offers a unique opportunity to probe the structure and atmosphere of an extrasolar ‘hot Neptune’. In this Letter, we present the main results of observations covering two transit events with the Near Infrared Camera and Multi Object Spectrograph (NICMOS) camera on the Hubble Space Telescope (HST). The data consist in high-cadence time series of grism spectra covering the 1.1–1.9 μm spectral range. We find Rpl= 4.04 ± 0.10 R⊕ and R*= 0.446 ± 0.011 R⊙ for the planet and star radius, confirming and improving earlier measurements with a ground-based photometry and a Spitzer light curve at 8 μm, as opposed to a much higher value obtained with the Fine Guidance Sensor on the HST. We measure no departure from strict periodicity in the transits to the level of ∼7 s. This strongly disfavours the proposed explanation of the orbital eccentricity of GJ 436b in terms of the perturbation by another close-by planet. We measure a flat transmission spectrum at the level of a few parts per 10 000 in flux, with no significant signal in the 1.4-μm water band to a level comparable to the maximum amplitude of the effect predicted by planetary atmosphere models.