Most of the existing algorithms for decimation of triangular meshes perform poorly at very low levels of detail. We propose a new automatic method for the decimation of triangular meshes, which performs better as compared to the notable existing algorithms at low levels of detail, preserves visually important parts of the mesh and thus keeps the semantic or high level meaning of the model. The proposed algorithm is based on greedy approach and exploites a new method of measuring geometric error employing a form of vertex visual importance that helps to keep visually impotant vertices even at low levels of detail and causes to remove other kinds of vertices, which do not profoundly influence the overall shape of the model. In addition, the proposed method has less momory overhead as compared to most of the published algorithms and is faster in terms of running times. The results of the algorithm have been compared numerically, visually, in terms of execution times and memory consumption with the sate-of-the-art decimation methods to strengthen the efficiency and quality of the algorithm.