Main purpose of this article is to consider the asymptotic distribution of the rank transformed F statistic for interaction in a two-way layout. Some theorems and sufficient conditions are derived to have the rank transformed F statistic converged in distribution to a chi-squared random variable with (I-1)(J-1) degrees of freedom divided by (I-1)(J-1). These results will be useful for the other theoretical studies of the rank transform procedure in experimental designs.