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In this paper, we propose a new feature descriptor for images that is based on the dihedral group D<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>4</mn> </msub> </semantics> </math> </inline-formula>, the symmetry group of the square. The group action of the D<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>4</mn> </msub> </semantics> </math> </inline-formula> elements on a square image region is used to create a vector space that forms the basis for the feature vector. For the evaluation, we employed the Error-Correcting Output Coding (ECOC) algorithm and tested our model with four diverse datasets. The results from the four databases used in this paper indicate that the feature vectors obtained from our proposed D<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>4</mn> </msub> </semantics> </math> </inline-formula> algorithm are comparable in performance to that of Histograms of Oriented Gradients (HOG) model. Furthermore, as the D<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>4</mn> </msub> </semantics> </math> </inline-formula> model encapsulates a complete set of orientations pertaining to the D<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>4</mn> </msub> </semantics> </math> </inline-formula> group, it enables its generalization to a wide range of image classification applications.