We have developed a new method for fabrication of single-crystal SiC-on-insulator using SIMOX (Separation by IMplanted OXygen) substrates. Carbonization of surface Si of SIMOX wafers induced cavities between the SiC and Si layers which resulted in low-quality SiC-on-insulator. On the other hand, crystalline SiC layers were formed on SIMOX substrates without cavities at SiC/Si interfaces by using CVD of SiC on as-implanted SIMOX substrates at 900 degreesC followed by N-2 annealing at 1350 degreesC.