A new polishing machine has been constructed for the fabrication of bonded-wafer silicon-on-insulator (bonded-wafer SOI) through a numerically controlled polishing technique. The polishing machine is equipped with 32 small-area tools which produce the variation of polishing pressure over a wafer surface. The tools do not rotate. Instead, the wafers being polished perform an oscillatory motion. A tool removal profile which was adequate for selectively polishing one place on a wafer without affecting its neighboring areas was obtained. As a result of its test operation, the initial thickness deviation of σ=380 nm of the top Si layer of a bonded-wafer SOI sample has been improved to σ=48 nm.