We study the effects of electron-electron interaction on the critical properties of the plateau transitions in the {\it integer} quantum Hall effect. We find the renormalization group dimension associated with short-range interactions to be $-0.66\pm0.04$. Thus the non-interacting fixed point (characterized $z=2$ and $��\approx 2.3$) is stable. For the Coulomb interaction, we find the correlation effect is a marginal perturbation at a Hartree-Fock fixed point ($z=1$, $��\approx 2.3$) by dimension counting. Further calculations are needed to determine its stability upon loop corrections.

12 pages, Revtex, minor changes, to be published in Phys. Rev. Lett