The conversion rate of nuclear spin isomers of water molecules in space is calculated using the model of quantum relaxation in the absence of particle collisions. The model is based on the intramolecular mixing of the ortho and para states of H2O by the spin-rotation interaction and on the interruption of the mixing by radiative transitions of a molecule in a thermal radiation field. The lifetime of water isomers at a thermal radiation temperature T = 50 K is ∼2 × 107 years, and at a temperature T = 100 K it is 3 × 106 years. The lifetimes of the spin isomers of water molecules are found to be large, but still smaller, for example, than the age of the Solar System. The proposed process of conversion of the spin isomers of water molecules is important for areas of space with low (n < 1 cm-3) particle concentrations.