  We demonstrate how one can construct renormalizable perturbative expansion in
formally nonrenormalizable higher dimensional scalar theories. It is based on
1/N-expansion and results in a logarithmically divergent perturbation theory in
arbitrary high odd space-time dimension. The resulting effective coupling is
dimensionless and is running in accordance with the usual RG equations. The
corresponding beta function is calculated in the leading order and is
nonpolynomial in effective coupling. It exhibits either UV asymptotically free
or IR free behaviour depending on the dimension of space-time.
