Nope, we even had a thread about this question not too long ago... although I can't seem to find it.
You can't just ADD speeds that way when dealing with relativisitic velocities. It works fine for slower relative velocities (like two cars passing one another on a racetrack) but not at all when the velocities approach light speed (like two particles passing one another in an accelerator).
The math is different, and in physics that's what counts. This website explains more, but is not really written for the layman, sadly.
http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html