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<p/> <p>The main purpose of this paper is to present some properties of the meromorphic solutions of complex difference equation of the form <inline-formula><graphic file="1687-1847-2010-404582-i1.gif"/></inline-formula>, where <inline-formula><graphic file="1687-1847-2010-404582-i2.gif"/></inline-formula> and <inline-formula><graphic file="1687-1847-2010-404582-i3.gif"/></inline-formula> are two finite index sets, <inline-formula><graphic file="1687-1847-2010-404582-i4.gif"/></inline-formula> are distinct, nonzero complex numbers, <inline-formula><graphic file="1687-1847-2010-404582-i5.gif"/></inline-formula> and <inline-formula><graphic file="1687-1847-2010-404582-i6.gif"/></inline-formula> are small functions relative to <inline-formula><graphic file="1687-1847-2010-404582-i7.gif"/></inline-formula> is a rational function in <inline-formula><graphic file="1687-1847-2010-404582-i8.gif"/></inline-formula> with coefficients which are small functions of <inline-formula><graphic file="1687-1847-2010-404582-i9.gif"/></inline-formula>. We also consider related complex functional equations in the paper.</p>