in this paper, we give some necessary conditions for a complex difference equation of malmquist type $$sum^n_{j=1}f(z+c_j)=frac{p(f(z))}{q(f(z))},$$ where $n(in{mathbb{n}})geq{2}$, and $p(f(z))$ and $q(f(z))$ are relatively prime polynomials in $f(z)$ with small functions as coefficients, admitting a meromorphic function of finite order. moreover, the properties of finite o...