The authors consider the difference equation competition system
\(x_{t+1}=x_{t}\dfrac{1+\phi _{1}(r_{1}\theta _{1}+\theta _{11}a_{11}x_{t}+\theta _{12}a_{12}y_{t})+\phi _{1}r_{1}}{1+\phi _{1}(r_{1}\theta _{1}+\theta _{11}a_{11}x_{t}+\theta _{12}a_{12}y_{t})+\phi _{1}(a_{11}x_{t}+a_{12}y_{t})},\)
\(y_{t+1}=y_{t}\dfrac{1+\phi _{2}(r_{2}\theta _{2}+\theta _{21}a_{21}x_{t}+\theta _{22}a_{22}y_{t})+\phi _{2}r_{2}}{1+\phi _{2}(r_{2}\theta _{2}+\theta _{21}a_{21}x_{t}+\theta _{22}a_{22}y_{t})+\phi _{2}(a_{21}x_{t}+a_{22}y_{t})}\),
where \(t=0,1,2,\dots,\) \(\phi _{i}>0\), \(\theta _{i}\geq 0\), \(\theta _{ij}\geq 0\), \(r_{i}>0\) and \(a_{ij}>0\) for all \(i,j=1,2\). This 2D map is derived using a non-standard finite difference method from the continuous time Lotka-Volterra competition system \(x^{\prime }=x(r_{1}-a_{11}x-a_{12}y)\), \(y^{\prime }=y(r_{2}-a_{21}x-a_{22}y)\). Then, under the condition that \(\theta _{11}\geq \theta _{12}\) and \(\theta _{22}\geq \theta _{21}\), the dynamics of the discrete system are almost the same as of the continuous system. The difference equations are dynamically consistent with their continuous counterparts. The positivity of solutions, monotonicity of solutions and stability conditions of equilibria are all preserved.