K. Fuchss, A. Wurm, P.J. Morrison On a new fixed point of the renormalization group operator for area-preserving maps (176K, RevTex with 5 PS figures) ABSTRACT. The breakup of the shearless invariant torus with winding number $\omega=\sqrt{2}-1$ is studied numerically using Greene's residue criterion in the standard nontwist map. The residue behavior and parameter scaling at the breakup suggests the existence of a new fixed point of the renormalization group operator (RGO) for area-preserving maps. The unstable eigenvalues of the RGO at this fixed point and the critical scaling exponents of the torus at breakup are computed.