Feature extraction plays a key role in pattern recognition problems. The texture feature is an important feature which helps to describe an image with textural information. A new texture descriptor, the Local Symmetric Tetra Pattern (LSTP), is proposed in this work. This descriptor is developed for the local description of an image. It considers not only the surrounding eight neighbors, but also the eight pixels at the next level to describe the texture efficiently. For every pixel, the maximum edge value, the number of negative sign bits and the number of positive sign bits for each degree of symmetry are computed. Image classification is experimented using the Original Brodatz, Outex and Kylberg Texture Dataset v.1.0 databases. The investigation results are compared with existing method which shows promising achievement of the proposed techniques in terms of their evaluation measures. It is also found that the proposed texture descriptor is rotationally invariant.