  Let $G$ be a finite group having a factorisation $G=AB$ into subgroups $A$
and $B$ with $B$ cyclic and $A\cap B=1,$ and let $b$ be a generator of $B$. The
associated skew-morphism is the bijective mapping $f:A \to A$ well defined by
the equality $baB=f(a)B$ where $a\in A$. In this paper, we shall classify all
skew-morphisms of cyclic $p$-groups where $p$ is an odd prime.
