In this note we study positive solutions of the mth order rational difference equation $x_n=(a_0+sum{{matop{i=1}}a_ix_{n-i}/(b_0+sum{{matop{i=1}}b_ix_{n-i}$, where n = m,m+1,m+2, $ldots$ and $x_0,ldots,x_{m-1}$ > 0. We describe a sufficient condition on nonnegative real numbers $a_0,a_1,ldots,a_m,b_0,b_1,ldots,b_m$ under which every solution $x_n$ of the above equation tends to the limit $(A-b_0+sqrt{(A-b_0)^2+4_{a_0}B}$/2B as $n{ ightarrow}{infty}$, where $A=sum{{matop{i=1}};a_i$ and $B=sum{{matop{i=1}};b_i$.