  In this paper we describe the automorphism groups of the endomorphism
semigroups of free Burnside groups $B(m,n)$ for odd exponents $n\ge1003$. We
prove, that the groups $Aut(End(B(m,n)))$ and $Aut(B(m,n))$ are isomorphic. In
particular, if the groups $Aut(End(B(m,n)))$ and $Aut(End(B(k,n)))$ are
isomorphic, then $m=k$.
