Process for preparing low-odor and storage-stable monomer-containing polyisocyanurates from isophorone diisocyanate, in which the partial trimerization is carried out over a period of from 2 minutes to 30 minutes in the presence of from 0.05 to 1.5% by weight, based on the weight of the diisocyanate, of a catalyst of the formula nullRnullNX3nullmnullnullmYnullwhere Ynull is a carboxylate anion having 4-8 carbon atoms, R is a null-hydroxyalkyl group having 2-6 carbon atoms and X is an alkylene group having from 2 to 3 carbon atoms and the three radicals X together with a shared nitrogen atom which may be partially null-hydroxyalkylated and the quaternary nitrogen form a tricyclic ring which may have an OH group in the null, null, or null position relative to the nitrogen and m is from 1.0 to 2.0, wherein the trimerization is carried out continuously in a tube reactor, in particular a reaction coil, in a temperature range of 20-120null C., and a pressure range from 0.5 to 5 bar and the catalyst is subsequently thermally deactivated at 100-160null C.