Given (and confirmed numerically) that the exponents&agr;and&bgr;in the passive scalar and velocity structure functions⟨(&Dgr;T3)a⟩∼r&agr;,and⟨(&Dgr;u3)a⟩∼r&bgr;are anomalous, the scaling of&ggr;in⟨(u(x+r)−u(x))a(T(x+r)−T(x))2a⟩∼r&ggr;is investigated. Analytical estimates show that&ggr;cannotbe as anomalous as&agr;or&bgr;.Numerical computations(Pr=1,Re&lgr;=141)show that&ggr;is closer to&bgr;than to&agr;.In addition, the statistical dependence of the velocity and passive scalar differences leads to anenhanced anomalyin&ggr;.©1998 American Institute of Physics.