The angular dependence of the nonlinear transverse magnetic moment of untwinned high-quality single crystals of optimally doped YBCO have been studied at a temperature of 2.5K using a low frequency AC technique. The absence of any signature at angular period 2pi/4is analyzed in light of the numerical predictions of such a signal for a pure d-wave order parameter with line nodes. Implications of this null result for the existence of a non-zero gap at all angles on the Fermi surface are discussed.