Permutation binomial functions over finite fields

We consider binomial functions over a finite field of order $2^n$. Some necessary condition is found for such a binomial function to be a permutation. It is proved that there are no permutation binomial functions in the case that $2^n-1$ is prime. Permutation binomial functions are constructed in the case when $4n$ is composite and found for $n\le8$. Tab. 2, bibliogr. 30.