In this paper, we present a novel method for local image descriptor called exact order based descriptor (EOD) which is robust to illumination changes and Gaussian noise. Exact orders of image patch is induced by changing discrete intensity value into k-dimensional continuous vector to resolve the ambiguity of ordering for same intensity pixel value. EOD is generated from overall distribution of exact orders in the patch. The proposed local descriptor is compared with several state-of-the-art descriptors over a number of images. Experimental results show that the proposed method outperforms many state-of-the-art descriptors in the presence of illumination changes, blur and viewpoint change. Also, the proposed method can be used for many computer vision applications such as face recognition, texture recognition and image analysis.