Physics FAQ:
http://www.phys.ncku.edu.tw/mirrors/physicsfaq/Relativity/SR/acceleration.html

"It is a common misconception that Special Relativity cannot handle accelerating objects or accelerating reference frames. It is claimed that general relativity is required because special relativity only applies to inertial frames. This is not true. Special relativity treats accelerating frames differently from inertial frames but can still deal with them. Accelerating objects can be dealt with without even calling upon accelerating frames."

:-)