The QUICKER formulation of the QUICK scheme is extended to a non-uniform rectangular grid system that can be widely adopted for the calculation of the flow problems of engineering interest. This new formulation is applied to obtain solutions of a one-dimensional non-linear Burgers equation and a two-dimensional lid-driven cavity flow. The computational results show that the new formulation is superior to existing schemes such as hybrid and skew-upwind-differencing, especially when the grid Peclet (or Reynolds) number is high.