We apply the prescription proposed in hep-th/0307197 for non-abelian expansion of S-matrix elements, to the S-matrix element of four tachyons and one gauge field in superstring theory. We show that the leading order terms of the expansion are in perfect agreement with the non-abelian generalization of the tachyon DBI action in which the tachyon potential is $V(T)=1+\\pi\\alpha\' m^2T^2+\\frac{1}{2!}(\\pi\\alpha\' m^2T^2)^2+...$ where $m^2=-1/(2\\alpha\')$ is the mass of tachyon. This calculation fixes the coefficient of $T^4$ in the potential without on-shell ambiguity.

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