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Consider the discrete Lasota-Wazewska modelNn+1-Nn=-μNn+pe-rNn-k, n=0,1,2,... (*)where μ∈(0,1),r,p∈(0,∞)and k∈N.A sufficient condiion for all positive solutions of (*)to be attracted to its equilibrium N*is obtained.It improves correspondent result obtained by Chen and Yu in 1999.