We describe observations of GRB050422, a Swift-discovered gamma-ray burst. The prompt gamma-ray emission had a T90 duration of 59 s and was multipeaked, with the main peak occurring at T + 53 s. Swift was able to follow the X-ray afterglow within 100 s of the burst trigger. The X-ray light curve, which shows a steep early decline, can be described by a broken power law with an initial decay slope of α1 ~ 5.0, a break time tb ~ 270 s and a post-break decay slope of α2 ~ 0.9, when the zero time of the X-ray emission is taken to be the burst trigger time. However, if the zero time is shifted to coincide with the onset of main peak in the gamma-ray light curve then the initial decay slope is shallower with α1 ~ 3.2. The initial gamma-ray spectrum can be modelled by a power law with a spectral index of βB = 0.50 +/- 0.19. However, the early time X-ray spectrum is significantly steeper than this and requires a spectral index of βX = 2.33+0.58-0.55.In comparison with other Swift bursts, GRB050422 was unusually X-ray faint, had a soft X-ray spectrum, and had an unusually steep early X-ray decline. Even so, its behaviour can be accommodated by standard models. The combined BAT/XRT light curve indicates that the initial, steeply declining, X-ray emission is related to the tail of the prompt gamma-ray emission. The shallower decay seen after the break is consistent with the standard afterglow model.