In terrain visualization, the quadtree is the most frequently used data structure for progressive mesh generation. The quadtree provides an efficient level-of-detail selection and view frustum culling. However, most applications using quadtrees are performed by the CPU, since the hierarchical data structure cannot be manipulated in a programmable rendering pipeline. For this reason, quadtree-based methods show lower performance and higher dependancy of CPU in comparison to GPU-based methods. We present a quadtree-based terrain-rendering method for GPU execution that uses vertex multiplication. It offers higher performance than previous CPU-based quadtree methods, without loss of image quality.