  We reconsider stability of the non-trivial fixed point in $6-\epsilon $
dimensional effective action for the random field Ising model derived by
Br\'{e}zin and De Dominicis. After expansion parameters of physical observables
are clarified, we find that the non-trivial fixed point in $6-\epsilon$
dimensions is stable, contrary to the argument by Br\'{e}zin and De Dominicis.
We also computed the exponents $\nu$ and $\eta$ by the $\epsilon$ expansion.
The results are consistent with the argument of the dimensional reduction at
least in the leading order.
