We introduce a fast simplification algorithm for terrain height fields to produce a triangulated irregular network, based on the greedy insertion algorithm in (Anjyo et al., 1992; Floriani et al., 1984; 1985). Our algorithm partitions terrain height data into rectangular blocks with the same size and simplifies blocks one by one with the greedy insertion algorithm. Our algorithm references only to the points and the triangles within each current block for adding a point into the triangulation. Therefore, our algorithm runs faster than the greedy insertion algorithm, which references all input points and triangles in the terrain. Our experiment shows that the partitioning method runs from 4 to more than 20 times faster and it approximates test height fields as accurately as the greedy insertion algorithms. Most greedy insertion algorithms suffer from elongated triangles that usually appear near the boundaries. However, we insert the four corner points into each block to produce the base triangulation of the block before the point addition step begins so that elongated triangles could not appear in the simplified terrain.