We have studied the optical properties of novel semiconductor nanosheets of Ti(1-delta)square(delta)O(2)(4 delta-) (delta similar to 0.09; square, vacancy) which were obtained by delaminating a layered titanate into elementary host layers. A uniform thickness in subnanometer scale as well as high crystallinity resulted in a sharp absorption onset with a well-developed peak assignable to excitonic transition. The absorption was pronouncedly blue shifted(> 1.4 eV) relative to the band edge for bulk TiO2, which is attributed to size quantization effects. Room-temperature photoluminescence spectra showed resonant emission and well-structured fluorescence extending into a lower energy region.