Starting from an organohydrogenpolysiloxane having at least two hydrogen atoms directly bonded to the silicone atoms, an organohydrogenpolysiloxane is obtained in which part of the silicon-bonded hydrogen atoms have been converted into organic groups and the remaining silicon-bonded hydrogen atoms are left unreacted. The starting organohydrogenpolysiloxane is brought to the partial addition reaction with less than equivalent amount of an organic unsaturated compound having aliphatic double bond in the molecule in the presence of a platinum catalyst, and the reaction mixture is subjected to distillation while the platinum catalyst is deactivated by added benzothiazole or derivatives thereof, thus providing for the production of the organohydrogenpolysiloxane of the invention in reproducibly in high yield. The compounds are useful as crosslinking agents in the manufacture of various silicone products.