The No Ghost Theorem in String Theory

A logically tight proof of the No Ghost Theorem for the standard bosonic open string theory is given, and an extension is established. The latter states that 26 is the critical dimension for all levels N = n > 2 of the number operator N in the sense that for any n > 2, there are no ghosts (negative norm states) on level N = n if and only if the dimension of spacetime is no greater than 26.