A map of the Moon at 2 cm wavelength is presented. The angular (≃ 1'arc) and temperature resolution (< 0.1 K) is sufficient to study systematic details of the brightness distribution. In particular, the centre-to-limb variation is considered. An estimate of the dielectric constant∈ is possible (1.4 ⩽∈ ⩽ 2.5). The existence of a temperature gradient in the lunar surface layers is used to derive the depth of penetration of electromagnetic waves (L e ), which isL e ≃ 8 m for 2 cm wavelength. The parameters derived from the 2 cm map are found to be compatible with those obtained from a former observation at 6 cm wavelength.