The effect of hydrogen-deuterium substitution on the rate of rotational diffusion of two species of amino-substituted anthraquinone dyes dissolved in the isotropic liquid phase of 4'-n-pentyl-4-cyanobiphenyl (5CB) and in a liquid mixture of alkanes (paraffin) has been studied as a function of temperature. The rotational dynamics was probed by time-resolved detection of fluorescence depolarization. In 5CB we observe a reduced rotational mobility of the deuterated species with respect to the protonated ones by up to 43% (at 311 K) and a corresponding increase of 4-5 kJ/mol in the activation energy, as deduced from the temperature dependence. To our knowledge, this is the largest isotopic effect ever reported for the molecular rotational diffusion in liquids. In liquid paraffin the effect vanishes. We attribute our findings to an isotopic effect in the breaking kinetics of the hydrogen-bond between the amino groups of dye molecules and the cyano group of 5CB that cannot be explained with the known isotopic effect of hydrogen-bond stability.