We present a floating-potential dielectrophoresis method used for the first time to achieve controlled alignment of an individual semiconducting or metallic single-walled carbon nanotube (SWCNT) between two electrical contacts with high repeatability. This result is significantly different from previous reports, in which bundles of SWCNTs were aligned between electrode arrays by a conventional dielectrophoresis process where the results were only collected from the control electrode regions. In this study, our alignment focus is not only on the regions of the control electrodes but also on those of the floating electrodes. Our results indicate that bundles of carbon nanotubes along with impurities were first moved into the region between two control electrodes while individual nanotubes without impurities were straightened and aligned between two floating electrodes. The measurements for the back-gated nanotube transistors made by this method displayed an on-off ratio and transconductance of 10(5) and 0.3 mu S, respectively. These output and transport properties are comparable with those of nanotube transistors made by other methods. Most importantly, the findings in this study show an effective way to separate individual nanotubes from bundles and impurities and advance the processes for site-selective fabrication of single-SWCNT transistors and related electrical devices.