We calculate the one-loop amplitude of the SO(32) type I superstring theory, using the covariant formulation. As a result we see the absence of the ln ε(ε→0) divergence in the parity-odd piece of the one-loop amplitude with the arbitrary number N of the external gauge bosons.
For completeness, we also include the proof of finiteness of the parity-even piece.
With the absence of the hexagon gauge anomaly, the above result gives the good perspective for the validity of the type I superstring theory.