Abstract: The GDOP (geometric dilutions of precision) is a key criterion to measure the graphic intensity of single-point-positioning configurations. Revealing the geometry of configurations with minimal GDOP has practical significance in the optimization design of single GNSS satellite constellation or multi-constellations. From the common used Walker configuration, we deduce a conditional equation to the combined Walker configurations to minimize the GDOP. The GDOP distribution on the surface of the Earth is discussed in terms of the conditional equation for minimizing the GDOP. Simulations were performed to verify the main results.