Hyers-Ulam stability of the difference equation with the initial point z0 as follows zi+1 = azi + b czi + d is investigated for complex numbers a, b, c and d where ad− bc = 1, c , 0 and a + d ∈ R [−2, 2]. The stability of the sequence {zn}n∈N0 holds if the initial point is in the exterior of a certain disk of which center is − dc . Furthermore, the region for stability can be extended to the complement of some neighborhood of the line segment between − dc and the repelling fixed point of the map z 7→ az+bcz+d . This result is the generalization of Hyers-Ulam stability of Pielou logistic equation.