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We investigate the local stability, prime period-two solutions, boundedness, invariant intervals, and global attractivity of all positive solutions of the following difference equation: 𝑦𝑛+1=(𝑟+𝑝𝑦𝑛+𝑦𝑛−𝑘)/(𝑞𝑦𝑛+𝑦𝑛−𝑘), 𝑛∈ℕ0, where the parameters 𝑝,𝑞,𝑟∈(0,∞),𝑘∈{1,2,3,…} and the initial conditions 𝑦−𝑘,…,𝑦0∈(0,∞). We show that the unique positive equilibrium of this equation is a global attractor under certain conditions.