The invention is directed to an improved, reliably performable process for preparing triallyl isocyanurate (TAIC) by Cu2+-catalysed rearrangement of triallyl cyanurate (TAC) at at least 90° C. According to the invention, TAC and, if required, also a Cu2+ catalyst and solvent are fed continuously to a start reaction mixture after onset of the initially inhibited isomerization reaction, the isomerization is performed at from 90 to 160° C. and an amount of reaction mixture equivalent to the amount of reactant is drawn off continuously and sent to the workup. Preference is given to effecting the isomerization in TAIC as the reaction medium.