  The R\'{e}dei function defined over a field of even characteristic has been
introduced by N\"{o}bauer in 1986 \cite{even}. In this paper, inspired by the
work of Fu et al. \cite{wang} in odd characteristic, employing the AGW
criterion \cite{agw}, we present a recursive construction of permutation
polynomials in even characteristic using the R\'{e}dei function over a field of
characteristic 2.
