  In this paper, we study the uniqueness of the difference of meromorphic
functions. We prove the following result: Let $f$ be a non-constant meromorphic
function of hyper-order less than $1$, let $\eta$ be a non-zero complex number,
$n\geq1$, an integer, and let $a,b,c\in\hat{S}(f)$ be three distinct small
functions and two of them be periodic small functions with period $\eta$. If
$f$ and $\Delta_{\eta}^{n}f$ share $a,b,c$ CM, then
$f\equiv\Delta_{\eta}^{n}f$.
