We report the discovery of NGTS-4b, a sub-Neptune-sized planet transiting a 13th magnitude K-dwarf in a 1.34d orbit. NGTS-4b has a mass M=$20.6pm3.0$M_E and radius R=$3.18pm0.26$R_E, which places it well within the so-called Neptunian Desert. The mean density of the planet ($3.45pm0.95$g/cm^3) is consistent with a composition of 100% H$_2$O or a rocky core with a volatile envelope. NGTS-4b is likely to suffer significant mass loss due to relatively strong EUV/X-ray irradiation. Its survival in the Neptunian desert may be due to an unusually high core mass, or it may have avoided the most intense X-ray irradiation by migrating after the initial activity of its host star had subsided. With a transit depth of $0.13pm0.02$%, NGTS-4b represents the shallowest transiting system ever discovered from the ground, and is the smallest planet discovered in a wide-field ground-based photometric survey.
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