  The $R_{\sigma,t}$-transform introduced by Bassa and Menares can be used to
construct families of irreducible polynomials in $\mathbb{F}_q[x]$. This
iterative construction is a generalization of Cohen's $R$-transform. For this
transform, Chapman proved that under some conditions, the polynomials in the
resulting family are completely normal. In this paper we establish conditions
ensuring that the polynomials obtained by using the $R_{\sigma,t}$-transform
are completely normal polynomials and we give a simple proof of Chapman's
result.
