In this remark, the authors consider the second-order linear difference equation
where is a real sequence with for . The main contribution is two-fold. One is to show that the main results of an earlier work by W. T. Li and S. S. Cheng [ibid. 16, No. 2, 161–163 (2003; Zbl 1052.39009)] are incorrect. The other is to obtain a generalized criterium about the oscillation and nonoscillation of the equation.