In this paper we introduce new bounds for robust stability analysis with real parameter uncertainty. The approach is based on an absolute stability criterion that excludes the Nyquist plot from a paraboloidal region containing the point −1 + _J0. Transformation of this criterion to the case of norm-bounded uncertainty leads to a stability criterion in terms of the octomorphic, or figure-eight shaped, region. The requirement that the Nyquist plot lie inside the octomorphic region thus yields a bound on the allowable real parameter uncertainty. This stability criterion is distinct from recent bounds for real-μ which involve frequency-dependent scales having a frequency-dependent, off-axis circle interpretation. Since the octomorphic region includes both upper and lower halves, it is able to encompass the entire Nyquist plot without using frequency-dependent scales.