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We analyze the Minimal Area solution to the Loop Equations in turbulence\cite{M93}. As it follows from the new derivation in the recent paper\cite{M19}, the vorticity is represented as a normal vector to the minimalsurface not just at the edge, like it was assumed before, but all over thesurface. As it was pointed in that paper, the self-consistency relation formean vorticity leads to $\alpha=\frac{1}{2}$, however the similar conditionsfor product of two and more vorticities cannot be satisfied without extraterms, which were left undetermined in that paper. In this paper we find thesemissing terms -- they are delta functions at coinciding points which must betaken into considerations in surface integrals. We compare this value of$\alpha$ with new measurements of the same team which confirmed the area law\cite{S19} and we find that asymptotic formula $\lambda(p) \approx 2 \alpha p +\beta \ln p$, with $\alpha =0.49 \pm 0.02, \beta= 0.92 \pm 0.01 $, fits alldata at $p=3,...10$ within error bars.

Scaling Index $\alpha = \frac{1}{2}$ In Turbulent Area Law