Calcite is the most abundant carbonate mineral in Earth's crust. Upon cleavage, the (10.4) plane with a rectangular unit cell is exposed. Interestingly, several experiments suggest a (2 × 1) surface reconstruction. However, clear experimental evidence and a theoretical confirmation were long missing. Recently, convincing indication for a (2 × 1) reconstruction has been given by atomic force microscopies taken at 5 K. Here, we show temperature-programmed desorption (TPD) experiments of water and ethanol desorbing from calcite (10.4) around room temperature. The TPD curves fit excellently to a kinetic model considering two different adsorption sites, as expected in case of a (2 × 1) reconstruction. This finding applies to the desorption of water and ethanol, illustrating that the effect is characteristic for the calcite cleavage plane. Our results thus show that the (2 × 1) reconstruction not only exists at room temperature but has significant impact on the interfacial properties of calcite.